KILLED proof of input_6ANRBjBsfK.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 307 ms] (2) CpxRelTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (8) CpxWeightedTrs (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedTrs (11) CompletionProof [UPPER BOUND(ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTypedWeightedCompleteTrs (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 21 ms] (16) CpxRNTS (17) SimplificationProof [BOTH BOUNDS(ID, ID), 35 ms] (18) CpxRNTS (19) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 90 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 22 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 3 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 172 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 13 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 59 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 4 ms] (44) CpxRNTS (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 244 ms] (48) CpxRNTS (49) IntTrsBoundProof [UPPER BOUND(ID), 85 ms] (50) CpxRNTS (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 341 ms] (54) CpxRNTS (55) IntTrsBoundProof [UPPER BOUND(ID), 95 ms] (56) CpxRNTS (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 462 ms] (60) CpxRNTS (61) IntTrsBoundProof [UPPER BOUND(ID), 73 ms] (62) CpxRNTS (63) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (64) CpxRNTS (65) IntTrsBoundProof [UPPER BOUND(ID), 99 ms] (66) CpxRNTS (67) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (68) CpxRNTS (69) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (70) CpxRNTS (71) IntTrsBoundProof [UPPER BOUND(ID), 750 ms] (72) CpxRNTS (73) IntTrsBoundProof [UPPER BOUND(ID), 193 ms] (74) CpxRNTS (75) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (76) CpxRNTS (77) IntTrsBoundProof [UPPER BOUND(ID), 127 ms] (78) CpxRNTS (79) IntTrsBoundProof [UPPER BOUND(ID), 43 ms] (80) CpxRNTS (81) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (82) CpxRNTS (83) IntTrsBoundProof [UPPER BOUND(ID), 127 ms] (84) CpxRNTS (85) IntTrsBoundProof [UPPER BOUND(ID), 12 ms] (86) CpxRNTS (87) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (88) CpxRNTS (89) IntTrsBoundProof [UPPER BOUND(ID), 32.5 s] (90) CpxRNTS (91) IntTrsBoundProof [UPPER BOUND(ID), 6388 ms] (92) CpxRNTS (93) CompletionProof [UPPER BOUND(ID), 0 ms] (94) CpxTypedWeightedCompleteTrs (95) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 24 ms] (96) CpxRNTS (97) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (98) CdtProblem (99) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (100) CdtProblem (101) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 365 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 31 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 41 ms] (124) CdtProblem (125) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 1 ms] (144) CdtProblem (145) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 138 ms] (148) CdtProblem (149) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 211 ms] (150) CdtProblem (151) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 166 ms] (152) CdtProblem (153) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 40 ms] (156) CdtProblem (157) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 1809 ms] (158) CdtProblem (159) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2221 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3566 ms] (172) CdtProblem (173) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2000 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 3004 ms] (176) CdtProblem (177) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 7396 ms] (178) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) turing(I(Halt, r), revltape, rtape, prog) -> rtape turing(Empty, revltape, rtape, prog) -> rtape lookup(S(x), I(l, r)) -> lookup(x, r) instrsConstrCheck(I(l1, r1), I(x, y)) -> True instrsConstrCheck(I(l1, r1), Empty) -> False instrsConstrCheck(Empty, I(x, y)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True instrConstrCheck(Goto(gtNat), Right) -> False instrConstrCheck(Goto(gtNat), Left) -> False instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False instrConstrCheck(Goto(gtNat), Halt) -> False instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Right, Goto(gtNat2)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(wNat2)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Left, Goto(gtNat2)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(wNat2)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False instrConstrCheck(Write(wNat), Right) -> False instrConstrCheck(Write(wNat), Left) -> False instrConstrCheck(Write(wNat), Write(wNat2)) -> True instrConstrCheck(Write(wNat), Halt) -> False instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Halt, Goto(gtNat2)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(wNat2)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lookup(0, instrs) -> instrs instrsSecond(I(l, r)) -> r instrsFirst(I(l, r)) -> l getWrite(Write(int)) -> int getGotoSecond(IfGoto(i1, i2)) -> i2 getGotoFirst(IfGoto(i1, i2)) -> i1 getGoto(Goto(int)) -> int run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) turing(I(Halt, r), revltape, rtape, prog) -> rtape turing(Empty, revltape, rtape, prog) -> rtape lookup(S(x), I(l, r)) -> lookup(x, r) instrsConstrCheck(I(l1, r1), I(x, y)) -> True instrsConstrCheck(I(l1, r1), Empty) -> False instrsConstrCheck(Empty, I(x, y)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True instrConstrCheck(Goto(gtNat), Right) -> False instrConstrCheck(Goto(gtNat), Left) -> False instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False instrConstrCheck(Goto(gtNat), Halt) -> False instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Right, Goto(gtNat2)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(wNat2)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Left, Goto(gtNat2)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(wNat2)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False instrConstrCheck(Write(wNat), Right) -> False instrConstrCheck(Write(wNat), Left) -> False instrConstrCheck(Write(wNat), Write(wNat2)) -> True instrConstrCheck(Write(wNat), Halt) -> False instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Halt, Goto(gtNat2)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(wNat2)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lookup(0, instrs) -> instrs instrsSecond(I(l, r)) -> r instrsFirst(I(l, r)) -> l getWrite(Write(int)) -> int getGotoSecond(IfGoto(i1, i2)) -> i2 getGotoFirst(IfGoto(i1, i2)) -> i1 getGoto(Goto(int)) -> int run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) turing(I(Halt, r), revltape, rtape, prog) -> rtape turing(Empty, revltape, rtape, prog) -> rtape lookup(S(x), I(l, r)) -> lookup(x, r) instrsConstrCheck(I(l1, r1), I(x, y)) -> True instrsConstrCheck(I(l1, r1), Empty) -> False instrsConstrCheck(Empty, I(x, y)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True instrConstrCheck(Goto(gtNat), Right) -> False instrConstrCheck(Goto(gtNat), Left) -> False instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False instrConstrCheck(Goto(gtNat), Halt) -> False instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Right, Goto(gtNat2)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(wNat2)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Left, Goto(gtNat2)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(wNat2)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False instrConstrCheck(Write(wNat), Right) -> False instrConstrCheck(Write(wNat), Left) -> False instrConstrCheck(Write(wNat), Write(wNat2)) -> True instrConstrCheck(Write(wNat), Halt) -> False instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Halt, Goto(gtNat2)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(wNat2)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lookup(0, instrs) -> instrs instrsSecond(I(l, r)) -> r instrsFirst(I(l, r)) -> l getWrite(Write(int)) -> int getGotoSecond(IfGoto(i1, i2)) -> i2 getGotoFirst(IfGoto(i1, i2)) -> i1 getGoto(Goto(int)) -> int run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0', revltape), Nil, prog) turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0', rtape), prog) turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) turing(I(Halt, r), revltape, rtape, prog) -> rtape turing(Empty, revltape, rtape, prog) -> rtape lookup(S(x), I(l, r)) -> lookup(x, r) instrsConstrCheck(I(l1, r1), I(x, y)) -> True instrsConstrCheck(I(l1, r1), Empty) -> False instrsConstrCheck(Empty, I(x, y)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True instrConstrCheck(Goto(gtNat), Right) -> False instrConstrCheck(Goto(gtNat), Left) -> False instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False instrConstrCheck(Goto(gtNat), Halt) -> False instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Right, Goto(gtNat2)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(wNat2)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Left, Goto(gtNat2)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(wNat2)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False instrConstrCheck(Write(wNat), Right) -> False instrConstrCheck(Write(wNat), Left) -> False instrConstrCheck(Write(wNat), Write(wNat2)) -> True instrConstrCheck(Write(wNat), Halt) -> False instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False instrConstrCheck(Halt, Goto(gtNat2)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(wNat2)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lookup(0', instrs) -> instrs instrsSecond(I(l, r)) -> r instrsFirst(I(l, r)) -> l getWrite(Write(int)) -> int getGotoSecond(IfGoto(i1, i2)) -> i2 getGotoFirst(IfGoto(i1, i2)) -> i1 getGoto(Goto(int)) -> int run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0', S(y)) -> False !EQ(S(x), 0') -> False !EQ(0', 0') -> True turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (7) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) [1] turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) [1] turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) [1] turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) [1] turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) [1] turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) [1] turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) [1] turing(I(Halt, r), revltape, rtape, prog) -> rtape [1] turing(Empty, revltape, rtape, prog) -> rtape [1] lookup(S(x), I(l, r)) -> lookup(x, r) [1] instrsConstrCheck(I(l1, r1), I(x, y)) -> True [1] instrsConstrCheck(I(l1, r1), Empty) -> False [1] instrsConstrCheck(Empty, I(x, y)) -> False [1] instrsConstrCheck(Empty, Empty) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False [1] instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True [1] instrConstrCheck(Goto(gtNat), Right) -> False [1] instrConstrCheck(Goto(gtNat), Left) -> False [1] instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False [1] instrConstrCheck(Goto(gtNat), Halt) -> False [1] instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Right, Goto(gtNat2)) -> False [1] instrConstrCheck(Right, Right) -> True [1] instrConstrCheck(Right, Left) -> False [1] instrConstrCheck(Right, Write(wNat2)) -> False [1] instrConstrCheck(Right, Halt) -> False [1] instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Left, Goto(gtNat2)) -> False [1] instrConstrCheck(Left, Right) -> False [1] instrConstrCheck(Left, Left) -> True [1] instrConstrCheck(Left, Write(wNat2)) -> False [1] instrConstrCheck(Left, Halt) -> False [1] instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False [1] instrConstrCheck(Write(wNat), Right) -> False [1] instrConstrCheck(Write(wNat), Left) -> False [1] instrConstrCheck(Write(wNat), Write(wNat2)) -> True [1] instrConstrCheck(Write(wNat), Halt) -> False [1] instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Halt, Goto(gtNat2)) -> False [1] instrConstrCheck(Halt, Right) -> False [1] instrConstrCheck(Halt, Left) -> False [1] instrConstrCheck(Halt, Write(wNat2)) -> False [1] instrConstrCheck(Halt, Halt) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] lookup(0, instrs) -> instrs [1] instrsSecond(I(l, r)) -> r [1] instrsFirst(I(l, r)) -> l [1] getWrite(Write(int)) -> int [1] getGotoSecond(IfGoto(i1, i2)) -> i2 [1] getGotoFirst(IfGoto(i1, i2)) -> i1 [1] getGoto(Goto(int)) -> int [1] run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) [1] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) [0] turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) [1] turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) [1] turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) [1] turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) [1] turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) [1] turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) [1] turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) [1] turing(I(Halt, r), revltape, rtape, prog) -> rtape [1] turing(Empty, revltape, rtape, prog) -> rtape [1] lookup(S(x), I(l, r)) -> lookup(x, r) [1] instrsConstrCheck(I(l1, r1), I(x, y)) -> True [1] instrsConstrCheck(I(l1, r1), Empty) -> False [1] instrsConstrCheck(Empty, I(x, y)) -> False [1] instrsConstrCheck(Empty, Empty) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False [1] instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True [1] instrConstrCheck(Goto(gtNat), Right) -> False [1] instrConstrCheck(Goto(gtNat), Left) -> False [1] instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False [1] instrConstrCheck(Goto(gtNat), Halt) -> False [1] instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Right, Goto(gtNat2)) -> False [1] instrConstrCheck(Right, Right) -> True [1] instrConstrCheck(Right, Left) -> False [1] instrConstrCheck(Right, Write(wNat2)) -> False [1] instrConstrCheck(Right, Halt) -> False [1] instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Left, Goto(gtNat2)) -> False [1] instrConstrCheck(Left, Right) -> False [1] instrConstrCheck(Left, Left) -> True [1] instrConstrCheck(Left, Write(wNat2)) -> False [1] instrConstrCheck(Left, Halt) -> False [1] instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False [1] instrConstrCheck(Write(wNat), Right) -> False [1] instrConstrCheck(Write(wNat), Left) -> False [1] instrConstrCheck(Write(wNat), Write(wNat2)) -> True [1] instrConstrCheck(Write(wNat), Halt) -> False [1] instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Halt, Goto(gtNat2)) -> False [1] instrConstrCheck(Halt, Right) -> False [1] instrConstrCheck(Halt, Left) -> False [1] instrConstrCheck(Halt, Write(wNat2)) -> False [1] instrConstrCheck(Halt, Halt) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] lookup(0, instrs) -> instrs [1] instrsSecond(I(l, r)) -> r [1] instrsFirst(I(l, r)) -> l [1] getWrite(Write(int)) -> int [1] getGotoSecond(IfGoto(i1, i2)) -> i2 [1] getGotoFirst(IfGoto(i1, i2)) -> i1 [1] getGoto(Goto(int)) -> int [1] run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) [1] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) [0] turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) [0] The TRS has the following type information: turing :: I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil I :: IfGoto:Goto:Right:Left:Write:Halt -> I:Empty -> I:Empty IfGoto :: 0:S -> 0:S -> IfGoto:Goto:Right:Left:Write:Halt Cons :: 0:S -> Cons:Nil -> Cons:Nil turing[Ite] :: True:False -> I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil !EQ :: 0:S -> 0:S -> True:False Goto :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt lookup :: 0:S -> I:Empty -> I:Empty Right :: IfGoto:Goto:Right:Left:Write:Halt Nil :: Cons:Nil 0 :: 0:S Left :: IfGoto:Goto:Right:Left:Write:Halt Write :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt Halt :: IfGoto:Goto:Right:Left:Write:Halt Empty :: I:Empty S :: 0:S -> 0:S instrsConstrCheck :: I:Empty -> I:Empty -> True:False True :: True:False False :: True:False instrConstrCheck :: IfGoto:Goto:Right:Left:Write:Halt -> IfGoto:Goto:Right:Left:Write:Halt -> True:False notEmpty :: Cons:Nil -> True:False instrsSecond :: I:Empty -> I:Empty instrsFirst :: I:Empty -> IfGoto:Goto:Right:Left:Write:Halt getWrite :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoSecond :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoFirst :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGoto :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S run :: I:Empty -> Cons:Nil -> Cons:Nil Rewrite Strategy: INNERMOST ---------------------------------------- (11) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: turing_4 instrsConstrCheck_2 instrConstrCheck_2 notEmpty_1 instrsSecond_1 instrsFirst_1 getWrite_1 getGotoSecond_1 getGotoFirst_1 getGoto_1 run_2 (c) The following functions are completely defined: lookup_2 !EQ_2 turing[Ite]_5 Due to the following rules being added: !EQ(v0, v1) -> null_!EQ [0] turing[Ite](v0, v1, v2, v3, v4) -> Nil [0] lookup(v0, v1) -> Empty [0] And the following fresh constants: null_!EQ ---------------------------------------- (12) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) [1] turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) [1] turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) [1] turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) [1] turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) [1] turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) [1] turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) [1] turing(I(Halt, r), revltape, rtape, prog) -> rtape [1] turing(Empty, revltape, rtape, prog) -> rtape [1] lookup(S(x), I(l, r)) -> lookup(x, r) [1] instrsConstrCheck(I(l1, r1), I(x, y)) -> True [1] instrsConstrCheck(I(l1, r1), Empty) -> False [1] instrsConstrCheck(Empty, I(x, y)) -> False [1] instrsConstrCheck(Empty, Empty) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False [1] instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True [1] instrConstrCheck(Goto(gtNat), Right) -> False [1] instrConstrCheck(Goto(gtNat), Left) -> False [1] instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False [1] instrConstrCheck(Goto(gtNat), Halt) -> False [1] instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Right, Goto(gtNat2)) -> False [1] instrConstrCheck(Right, Right) -> True [1] instrConstrCheck(Right, Left) -> False [1] instrConstrCheck(Right, Write(wNat2)) -> False [1] instrConstrCheck(Right, Halt) -> False [1] instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Left, Goto(gtNat2)) -> False [1] instrConstrCheck(Left, Right) -> False [1] instrConstrCheck(Left, Left) -> True [1] instrConstrCheck(Left, Write(wNat2)) -> False [1] instrConstrCheck(Left, Halt) -> False [1] instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False [1] instrConstrCheck(Write(wNat), Right) -> False [1] instrConstrCheck(Write(wNat), Left) -> False [1] instrConstrCheck(Write(wNat), Write(wNat2)) -> True [1] instrConstrCheck(Write(wNat), Halt) -> False [1] instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Halt, Goto(gtNat2)) -> False [1] instrConstrCheck(Halt, Right) -> False [1] instrConstrCheck(Halt, Left) -> False [1] instrConstrCheck(Halt, Write(wNat2)) -> False [1] instrConstrCheck(Halt, Halt) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] lookup(0, instrs) -> instrs [1] instrsSecond(I(l, r)) -> r [1] instrsFirst(I(l, r)) -> l [1] getWrite(Write(int)) -> int [1] getGotoSecond(IfGoto(i1, i2)) -> i2 [1] getGotoFirst(IfGoto(i1, i2)) -> i1 [1] getGoto(Goto(int)) -> int [1] run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) [1] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) [0] turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) [0] !EQ(v0, v1) -> null_!EQ [0] turing[Ite](v0, v1, v2, v3, v4) -> Nil [0] lookup(v0, v1) -> Empty [0] The TRS has the following type information: turing :: I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil I :: IfGoto:Goto:Right:Left:Write:Halt -> I:Empty -> I:Empty IfGoto :: 0:S -> 0:S -> IfGoto:Goto:Right:Left:Write:Halt Cons :: 0:S -> Cons:Nil -> Cons:Nil turing[Ite] :: True:False:null_!EQ -> I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil !EQ :: 0:S -> 0:S -> True:False:null_!EQ Goto :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt lookup :: 0:S -> I:Empty -> I:Empty Right :: IfGoto:Goto:Right:Left:Write:Halt Nil :: Cons:Nil 0 :: 0:S Left :: IfGoto:Goto:Right:Left:Write:Halt Write :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt Halt :: IfGoto:Goto:Right:Left:Write:Halt Empty :: I:Empty S :: 0:S -> 0:S instrsConstrCheck :: I:Empty -> I:Empty -> True:False:null_!EQ True :: True:False:null_!EQ False :: True:False:null_!EQ instrConstrCheck :: IfGoto:Goto:Right:Left:Write:Halt -> IfGoto:Goto:Right:Left:Write:Halt -> True:False:null_!EQ notEmpty :: Cons:Nil -> True:False:null_!EQ instrsSecond :: I:Empty -> I:Empty instrsFirst :: I:Empty -> IfGoto:Goto:Right:Left:Write:Halt getWrite :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoSecond :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoFirst :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGoto :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S run :: I:Empty -> Cons:Nil -> Cons:Nil null_!EQ :: True:False:null_!EQ Rewrite Strategy: INNERMOST ---------------------------------------- (13) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (14) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: turing(I(IfGoto(S(y'), i2), r), revltape, Cons(S(x'), xs), prog) -> turing[Ite](!EQ(x', y'), I(IfGoto(S(y'), i2), r), revltape, Cons(S(x'), xs), prog) [1] turing(I(IfGoto(S(y''), i2), r), revltape, Cons(0, xs), prog) -> turing[Ite](False, I(IfGoto(S(y''), i2), r), revltape, Cons(0, xs), prog) [1] turing(I(IfGoto(0, i2), r), revltape, Cons(S(x''), xs), prog) -> turing[Ite](False, I(IfGoto(0, i2), r), revltape, Cons(S(x''), xs), prog) [1] turing(I(IfGoto(0, i2), r), revltape, Cons(0, xs), prog) -> turing[Ite](True, I(IfGoto(0, i2), r), revltape, Cons(0, xs), prog) [1] turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](null_!EQ, I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) [1] turing(I(Goto(S(x1)), r), revltape, rtape, I(l', r')) -> turing(lookup(x1, r'), revltape, rtape, I(l', r')) [2] turing(I(Goto(0), r), revltape, rtape, prog) -> turing(prog, revltape, rtape, prog) [2] turing(I(Goto(int), r), revltape, rtape, prog) -> turing(Empty, revltape, rtape, prog) [1] turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) [1] turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) [1] turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) [1] turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) [1] turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) [1] turing(I(Halt, r), revltape, rtape, prog) -> rtape [1] turing(Empty, revltape, rtape, prog) -> rtape [1] lookup(S(x), I(l, r)) -> lookup(x, r) [1] instrsConstrCheck(I(l1, r1), I(x, y)) -> True [1] instrsConstrCheck(I(l1, r1), Empty) -> False [1] instrsConstrCheck(Empty, I(x, y)) -> False [1] instrsConstrCheck(Empty, Empty) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False [1] instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True [1] instrConstrCheck(Goto(gtNat), Right) -> False [1] instrConstrCheck(Goto(gtNat), Left) -> False [1] instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False [1] instrConstrCheck(Goto(gtNat), Halt) -> False [1] instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Right, Goto(gtNat2)) -> False [1] instrConstrCheck(Right, Right) -> True [1] instrConstrCheck(Right, Left) -> False [1] instrConstrCheck(Right, Write(wNat2)) -> False [1] instrConstrCheck(Right, Halt) -> False [1] instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Left, Goto(gtNat2)) -> False [1] instrConstrCheck(Left, Right) -> False [1] instrConstrCheck(Left, Left) -> True [1] instrConstrCheck(Left, Write(wNat2)) -> False [1] instrConstrCheck(Left, Halt) -> False [1] instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False [1] instrConstrCheck(Write(wNat), Right) -> False [1] instrConstrCheck(Write(wNat), Left) -> False [1] instrConstrCheck(Write(wNat), Write(wNat2)) -> True [1] instrConstrCheck(Write(wNat), Halt) -> False [1] instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Halt, Goto(gtNat2)) -> False [1] instrConstrCheck(Halt, Right) -> False [1] instrConstrCheck(Halt, Left) -> False [1] instrConstrCheck(Halt, Write(wNat2)) -> False [1] instrConstrCheck(Halt, Halt) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] lookup(0, instrs) -> instrs [1] instrsSecond(I(l, r)) -> r [1] instrsFirst(I(l, r)) -> l [1] getWrite(Write(int)) -> int [1] getGotoSecond(IfGoto(i1, i2)) -> i2 [1] getGotoFirst(IfGoto(i1, i2)) -> i1 [1] getGoto(Goto(int)) -> int [1] run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) [1] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] turing[Ite](True, I(IfGoto(i1, S(x2)), r), revltape, rtape, I(l'', r'')) -> turing(lookup(x2, r''), revltape, rtape, I(l'', r'')) [1] turing[Ite](True, I(IfGoto(i1, 0), r), revltape, rtape, prog) -> turing(prog, revltape, rtape, prog) [1] turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(Empty, revltape, rtape, prog) [0] turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) [0] !EQ(v0, v1) -> null_!EQ [0] turing[Ite](v0, v1, v2, v3, v4) -> Nil [0] lookup(v0, v1) -> Empty [0] The TRS has the following type information: turing :: I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil I :: IfGoto:Goto:Right:Left:Write:Halt -> I:Empty -> I:Empty IfGoto :: 0:S -> 0:S -> IfGoto:Goto:Right:Left:Write:Halt Cons :: 0:S -> Cons:Nil -> Cons:Nil turing[Ite] :: True:False:null_!EQ -> I:Empty -> Cons:Nil -> Cons:Nil -> I:Empty -> Cons:Nil !EQ :: 0:S -> 0:S -> True:False:null_!EQ Goto :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt lookup :: 0:S -> I:Empty -> I:Empty Right :: IfGoto:Goto:Right:Left:Write:Halt Nil :: Cons:Nil 0 :: 0:S Left :: IfGoto:Goto:Right:Left:Write:Halt Write :: 0:S -> IfGoto:Goto:Right:Left:Write:Halt Halt :: IfGoto:Goto:Right:Left:Write:Halt Empty :: I:Empty S :: 0:S -> 0:S instrsConstrCheck :: I:Empty -> I:Empty -> True:False:null_!EQ True :: True:False:null_!EQ False :: True:False:null_!EQ instrConstrCheck :: IfGoto:Goto:Right:Left:Write:Halt -> IfGoto:Goto:Right:Left:Write:Halt -> True:False:null_!EQ notEmpty :: Cons:Nil -> True:False:null_!EQ instrsSecond :: I:Empty -> I:Empty instrsFirst :: I:Empty -> IfGoto:Goto:Right:Left:Write:Halt getWrite :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoSecond :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGotoFirst :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S getGoto :: IfGoto:Goto:Right:Left:Write:Halt -> 0:S run :: I:Empty -> Cons:Nil -> Cons:Nil null_!EQ :: True:False:null_!EQ Rewrite Strategy: INNERMOST ---------------------------------------- (15) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: Right => 2 Nil => 0 0 => 0 Left => 1 Halt => 0 Empty => 0 True => 2 False => 1 null_!EQ => 0 ---------------------------------------- (16) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x getGoto(z) -{ 1 }-> int :|: int >= 0, z = 1 + int getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> int :|: int >= 0, z = 1 + int instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1 + gtNat, z' = 1 + gtNat2, gtNat2 >= 0, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: wNat >= 0, z' = 1 + wNat2, wNat2 >= 0, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 1 + gtNat2, z = 1 + igtNat1 + igtNat2, gtNat2 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1 + wNat2, wNat2 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, igtNat12 >= 0, igtNat22 >= 0, gtNat >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, z' = 2, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, gtNat >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, z' = 1 + wNat2, wNat2 >= 0, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, gtNat >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 + gtNat2, gtNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 + wNat2, wNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + gtNat2, z = 1, gtNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 1 + wNat2, wNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, igtNat12 >= 0, igtNat22 >= 0, z = 1 + wNat, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z' = 1 + gtNat2, gtNat2 >= 0, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z' = 2, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z = 1 + wNat, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z = 1 + wNat, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + gtNat2, gtNat2 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + wNat2, wNat2 >= 0, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> instrs :|: instrs >= 0, z' = instrs, z = 0 lookup(z, z') -{ 1 }-> lookup(x, r) :|: r >= 0, x >= 0, z' = 1 + l + r, l >= 0, z = 1 + x lookup(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(prog, 0, tapeinput, prog) :|: tapeinput >= 0, z = prog, prog >= 0, z' = tapeinput turing(z, z', z'', z1) -{ 1 }-> rtape :|: r >= 0, z = 1 + 0 + r, prog >= 0, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape turing(z, z', z'', z1) -{ 1 }-> rtape :|: prog >= 0, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, revltape, 1 + 0 + xs, prog) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, xs >= 0, z'' = 1 + 0 + xs, prog >= 0, z1 = prog, revltape >= 0, z' = revltape, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, revltape, 1 + (1 + x'') + xs, prog) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, prog >= 0, z1 = prog, revltape >= 0, z' = revltape, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, revltape, 1 + 0 + xs, prog) :|: r >= 0, xs >= 0, z = 1 + (1 + (1 + y'') + i2) + r, z'' = 1 + 0 + xs, y'' >= 0, prog >= 0, z1 = prog, revltape >= 0, z' = revltape, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, revltape, 1 + x + xs, prog) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, prog >= 0, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, revltape, 1 + (1 + x') + xs, prog) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, prog >= 0, z1 = prog, revltape >= 0, z' = revltape, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(prog, revltape, rtape, prog) :|: r >= 0, prog >= 0, z1 = prog, z = 1 + (1 + 0) + r, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape turing(z, z', z'', z1) -{ 1 }-> turing(r, revltape, 1 + int + xs, prog) :|: r >= 0, xs >= 0, x >= 0, prog >= 0, z = 1 + (1 + int) + r, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, xs, 1 + x + rtape, prog) :|: r >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, prog >= 0, z1 = prog, rtape >= 0, z'' = rtape, z = 1 + 1 + r turing(z, z', z'', z1) -{ 1 }-> turing(r, 0, 1 + 0 + rtape, prog) :|: r >= 0, prog >= 0, z1 = prog, rtape >= 0, z'' = rtape, z = 1 + 1 + r, z' = 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, 1 + x + revltape, xs, prog) :|: r >= 0, xs >= 0, x >= 0, prog >= 0, z = 1 + 2 + r, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape turing(z, z', z'', z1) -{ 1 }-> turing(r, 1 + 0 + revltape, 0, prog) :|: z'' = 0, r >= 0, prog >= 0, z = 1 + 2 + r, z1 = prog, revltape >= 0, z' = revltape turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), revltape, rtape, 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, revltape, rtape, prog) :|: r >= 0, prog >= 0, z = 1 + (1 + int) + r, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape, int >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(prog, revltape, rtape, prog) :|: z = 2, r >= 0, i1 >= 0, prog >= 0, z1 = rtape, rtape >= 0, revltape >= 0, z2 = prog, z' = 1 + (1 + i1 + 0) + r, z'' = revltape turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, revltape, rtape, prog) :|: r >= 0, z = 1, z' = 1 + l + r, prog >= 0, l >= 0, z1 = rtape, rtape >= 0, revltape >= 0, z2 = prog, z'' = revltape turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), revltape, rtape, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 = rtape, rtape >= 0, r'' >= 0, revltape >= 0, z'' = revltape, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, revltape, rtape, prog) :|: z = 2, r >= 0, i1 >= 0, prog >= 0, z1 = rtape, rtape >= 0, revltape >= 0, z2 = prog, z'' = revltape, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 ---------------------------------------- (17) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (18) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 ---------------------------------------- (19) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { instrsFirst } { instrsSecond } { notEmpty } { getWrite } { instrsConstrCheck } { lookup } { !EQ } { getGotoSecond } { instrConstrCheck } { getGotoFirst } { getGoto } { turing[Ite], turing } { run } ---------------------------------------- (20) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsFirst}, {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} ---------------------------------------- (21) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (22) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsFirst}, {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} ---------------------------------------- (23) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: instrsFirst after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (24) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsFirst}, {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: ?, size: O(n^1) [z] ---------------------------------------- (25) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: instrsFirst after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (27) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (29) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: instrsSecond after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsSecond}, {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: ?, size: O(n^1) [z] ---------------------------------------- (31) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: instrsSecond after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (33) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (35) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: notEmpty after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {notEmpty}, {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: ?, size: O(1) [2] ---------------------------------------- (37) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: notEmpty after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (39) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (40) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (41) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getWrite after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (42) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getWrite}, {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: ?, size: O(n^1) [z] ---------------------------------------- (43) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getWrite after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (44) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (45) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (46) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (47) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: instrsConstrCheck after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (48) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrsConstrCheck}, {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: ?, size: O(1) [2] ---------------------------------------- (49) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: instrsConstrCheck after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (50) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (51) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (52) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (53) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: lookup after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z' ---------------------------------------- (54) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {lookup}, {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: ?, size: O(n^1) [z'] ---------------------------------------- (55) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using KoAT for: lookup after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: 1 + z' ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 1 }-> lookup(z - 1, r) :|: r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 2 }-> turing(lookup(x1, r'), z', z'', 1 + l' + r') :|: r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(lookup(x2, r''), z'', z1, 1 + l'' + r'') :|: z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] ---------------------------------------- (57) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (58) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] ---------------------------------------- (59) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: !EQ after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {!EQ}, {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: ?, size: O(1) [2] ---------------------------------------- (61) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: !EQ after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 !EQ(z, z') -{ 0 }-> !EQ(z - 1, z' - 1) :|: z - 1 >= 0, z' - 1 >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x', y'), 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (63) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] ---------------------------------------- (65) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getGotoSecond after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoSecond}, {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: ?, size: O(n^1) [z] ---------------------------------------- (67) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getGotoSecond after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (69) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (71) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: instrConstrCheck after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 2 ---------------------------------------- (72) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {instrConstrCheck}, {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: ?, size: O(1) [2] ---------------------------------------- (73) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: instrConstrCheck after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (74) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (75) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (76) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] ---------------------------------------- (77) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getGotoFirst after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (78) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGotoFirst}, {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: ?, size: O(n^1) [z] ---------------------------------------- (79) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getGotoFirst after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (80) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (81) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (82) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (83) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: getGoto after applying outer abstraction to obtain an ITS, resulting in: O(n^1) with polynomial bound: z ---------------------------------------- (84) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {getGoto}, {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] getGoto: runtime: ?, size: O(n^1) [z] ---------------------------------------- (85) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: getGoto after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (86) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] getGoto: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (87) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (88) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] getGoto: runtime: O(1) [1], size: O(n^1) [z] ---------------------------------------- (89) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using CoFloCo for: turing[Ite] after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? Computed SIZE bound using CoFloCo for: turing after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (90) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] getGoto: runtime: O(1) [1], size: O(n^1) [z] turing[Ite]: runtime: ?, size: INF turing: runtime: ?, size: INF ---------------------------------------- (91) IntTrsBoundProof (UPPER BOUND(ID)) Computed RUNTIME bound using CoFloCo for: turing[Ite] after applying outer abstraction to obtain an ITS, resulting in: INF with polynomial bound: ? ---------------------------------------- (92) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> s2 :|: s2 >= 0, s2 <= 2, z - 1 >= 0, z' - 1 >= 0 !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' - 1 >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: z - 1 >= 0, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 getGoto(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getWrite(z) -{ 1 }-> z - 1 :|: z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' - 1 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z - 1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z - 1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' - 1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' - 1 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 lookup(z, z') -{ 2 + r }-> s' :|: s' >= 0, s' <= r, r >= 0, z - 1 >= 0, z' = 1 + l + r, l >= 0 lookup(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 lookup(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 run(z, z') -{ 1 }-> turing(z, 0, z', z) :|: z' >= 0, z >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z - 1 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> z'' :|: z1 >= 0, z'' >= 0, z' >= 0, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](s1, 1 + (1 + (1 + y') + i2) + r, z', 1 + (1 + x') + xs, z1) :|: s1 >= 0, s1 <= 2, r >= 0, xs >= 0, z'' = 1 + (1 + x') + xs, x' >= 0, y' >= 0, z1 >= 0, z' >= 0, z = 1 + (1 + (1 + y') + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](2, 1 + (1 + 0 + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: z = 1 + (1 + 0 + i2) + r, r >= 0, z'' - 1 >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + 0 + i2) + r, z', 1 + (1 + x'') + xs, z1) :|: z = 1 + (1 + 0 + i2) + r, z'' = 1 + (1 + x'') + xs, r >= 0, xs >= 0, z1 >= 0, z' >= 0, x'' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](1, 1 + (1 + (1 + y'') + i2) + r, z', 1 + 0 + (z'' - 1), z1) :|: r >= 0, z'' - 1 >= 0, z = 1 + (1 + (1 + y'') + i2) + r, y'' >= 0, z1 >= 0, z' >= 0, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](0, 1 + (1 + i1 + i2) + r, z', 1 + x + xs, z1) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, z', 1 + int + xs, z1) :|: r >= 0, xs >= 0, x >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' = 1 + x + xs, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 3 + r' }-> turing(s, z', z'', 1 + l' + r') :|: s >= 0, s <= r', r >= 0, x1 >= 0, l' >= 0, r' >= 0, z1 = 1 + l' + r', z'' >= 0, z' >= 0, z = 1 + (1 + (1 + x1)) + r turing(z, z', z'', z1) -{ 2 }-> turing(z1, z', z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(0, z', z'', z1) :|: r >= 0, z1 >= 0, z = 1 + (1 + int) + r, z'' >= 0, z' >= 0, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + x + z', xs, z1) :|: z - 3 >= 0, xs >= 0, x >= 0, z1 >= 0, z'' = 1 + x + xs, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 3, 1 + 0 + z', 0, z1) :|: z'' = 0, z - 3 >= 0, z1 >= 0, z' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, xs, 1 + x + z'', z1) :|: z - 2 >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, z1 >= 0, z'' >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(z - 2, 0, 1 + 0 + z'', z1) :|: z - 2 >= 0, z1 >= 0, z'' >= 0, z' = 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, z'', z1, z2) :|: r >= 0, z = 1, z' = 1 + l + r, z2 >= 0, l >= 0, z1 >= 0, z'' >= 0 turing[Ite](z, z', z'', z1, z2) -{ 2 + r'' }-> turing(s'', z'', z1, 1 + l'' + r'') :|: s'' >= 0, s'' <= r'', z = 2, r >= 0, i1 >= 0, l'' >= 0, z' = 1 + (1 + i1 + (1 + x2)) + r, z1 >= 0, r'' >= 0, z'' >= 0, x2 >= 0, z2 = 1 + l'' + r'' turing[Ite](z, z', z'', z1, z2) -{ 1 }-> turing(z2, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, z' = 1 + (1 + i1 + 0) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(0, z'', z1, z2) :|: z = 2, r >= 0, i1 >= 0, z2 >= 0, z1 >= 0, z'' >= 0, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z >= 0, z2 >= 0, z' >= 0, z'' >= 0, z1 >= 0 Function symbols to be analyzed: {turing[Ite],turing}, {run} Previous analysis results are: instrsFirst: runtime: O(1) [1], size: O(n^1) [z] instrsSecond: runtime: O(1) [1], size: O(n^1) [z] notEmpty: runtime: O(1) [1], size: O(1) [2] getWrite: runtime: O(1) [1], size: O(n^1) [z] instrsConstrCheck: runtime: O(1) [1], size: O(1) [2] lookup: runtime: O(n^1) [1 + z'], size: O(n^1) [z'] !EQ: runtime: O(1) [0], size: O(1) [2] getGotoSecond: runtime: O(1) [1], size: O(n^1) [z] instrConstrCheck: runtime: O(1) [1], size: O(1) [2] getGotoFirst: runtime: O(1) [1], size: O(n^1) [z] getGoto: runtime: O(1) [1], size: O(n^1) [z] turing[Ite]: runtime: INF, size: INF turing: runtime: ?, size: INF ---------------------------------------- (93) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: !EQ(v0, v1) -> null_!EQ [0] turing[Ite](v0, v1, v2, v3, v4) -> null_turing[Ite] [0] turing(v0, v1, v2, v3) -> null_turing [0] lookup(v0, v1) -> null_lookup [0] notEmpty(v0) -> null_notEmpty [0] instrsSecond(v0) -> null_instrsSecond [0] instrsFirst(v0) -> null_instrsFirst [0] getWrite(v0) -> null_getWrite [0] getGotoSecond(v0) -> null_getGotoSecond [0] getGotoFirst(v0) -> null_getGotoFirst [0] getGoto(v0) -> null_getGoto [0] instrsConstrCheck(v0, v1) -> null_instrsConstrCheck [0] instrConstrCheck(v0, v1) -> null_instrConstrCheck [0] And the following fresh constants: null_!EQ, null_turing[Ite], null_turing, null_lookup, null_notEmpty, null_instrsSecond, null_instrsFirst, null_getWrite, null_getGotoSecond, null_getGotoFirst, null_getGoto, null_instrsConstrCheck, null_instrConstrCheck ---------------------------------------- (94) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: turing(I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) -> turing[Ite](!EQ(x, i1), I(IfGoto(i1, i2), r), revltape, Cons(x, xs), prog) [1] turing(I(Goto(int), r), revltape, rtape, prog) -> turing(lookup(int, prog), revltape, rtape, prog) [1] turing(I(Right, r), revltape, Cons(x, xs), prog) -> turing(r, Cons(x, revltape), xs, prog) [1] turing(I(Right, r), revltape, Nil, prog) -> turing(r, Cons(0, revltape), Nil, prog) [1] turing(I(Left, r), Cons(x, xs), rtape, prog) -> turing(r, xs, Cons(x, rtape), prog) [1] turing(I(Left, r), Nil, rtape, prog) -> turing(r, Nil, Cons(0, rtape), prog) [1] turing(I(Write(int), r), revltape, Cons(x, xs), prog) -> turing(r, revltape, Cons(int, xs), prog) [1] turing(I(Halt, r), revltape, rtape, prog) -> rtape [1] turing(Empty, revltape, rtape, prog) -> rtape [1] lookup(S(x), I(l, r)) -> lookup(x, r) [1] instrsConstrCheck(I(l1, r1), I(x, y)) -> True [1] instrsConstrCheck(I(l1, r1), Empty) -> False [1] instrsConstrCheck(Empty, I(x, y)) -> False [1] instrsConstrCheck(Empty, Empty) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), IfGoto(igtNat12, igtNat22)) -> True [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Goto(gtNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Right) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Left) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Write(wNat2)) -> False [1] instrConstrCheck(IfGoto(igtNat1, igtNat2), Halt) -> False [1] instrConstrCheck(Goto(gtNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Goto(gtNat), Goto(gtNat2)) -> True [1] instrConstrCheck(Goto(gtNat), Right) -> False [1] instrConstrCheck(Goto(gtNat), Left) -> False [1] instrConstrCheck(Goto(gtNat), Write(wNat2)) -> False [1] instrConstrCheck(Goto(gtNat), Halt) -> False [1] instrConstrCheck(Right, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Right, Goto(gtNat2)) -> False [1] instrConstrCheck(Right, Right) -> True [1] instrConstrCheck(Right, Left) -> False [1] instrConstrCheck(Right, Write(wNat2)) -> False [1] instrConstrCheck(Right, Halt) -> False [1] instrConstrCheck(Left, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Left, Goto(gtNat2)) -> False [1] instrConstrCheck(Left, Right) -> False [1] instrConstrCheck(Left, Left) -> True [1] instrConstrCheck(Left, Write(wNat2)) -> False [1] instrConstrCheck(Left, Halt) -> False [1] instrConstrCheck(Write(wNat), IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Write(wNat), Goto(gtNat2)) -> False [1] instrConstrCheck(Write(wNat), Right) -> False [1] instrConstrCheck(Write(wNat), Left) -> False [1] instrConstrCheck(Write(wNat), Write(wNat2)) -> True [1] instrConstrCheck(Write(wNat), Halt) -> False [1] instrConstrCheck(Halt, IfGoto(igtNat12, igtNat22)) -> False [1] instrConstrCheck(Halt, Goto(gtNat2)) -> False [1] instrConstrCheck(Halt, Right) -> False [1] instrConstrCheck(Halt, Left) -> False [1] instrConstrCheck(Halt, Write(wNat2)) -> False [1] instrConstrCheck(Halt, Halt) -> True [1] notEmpty(Cons(x, xs)) -> True [1] notEmpty(Nil) -> False [1] lookup(0, instrs) -> instrs [1] instrsSecond(I(l, r)) -> r [1] instrsFirst(I(l, r)) -> l [1] getWrite(Write(int)) -> int [1] getGotoSecond(IfGoto(i1, i2)) -> i2 [1] getGotoFirst(IfGoto(i1, i2)) -> i1 [1] getGoto(Goto(int)) -> int [1] run(prog, tapeinput) -> turing(prog, Nil, tapeinput, prog) [1] !EQ(S(x), S(y)) -> !EQ(x, y) [0] !EQ(0, S(y)) -> False [0] !EQ(S(x), 0) -> False [0] !EQ(0, 0) -> True [0] turing[Ite](True, I(IfGoto(i1, i2), r), revltape, rtape, prog) -> turing(lookup(i2, prog), revltape, rtape, prog) [0] turing[Ite](False, I(l, r), revltape, rtape, prog) -> turing(r, revltape, rtape, prog) [0] !EQ(v0, v1) -> null_!EQ [0] turing[Ite](v0, v1, v2, v3, v4) -> null_turing[Ite] [0] turing(v0, v1, v2, v3) -> null_turing [0] lookup(v0, v1) -> null_lookup [0] notEmpty(v0) -> null_notEmpty [0] instrsSecond(v0) -> null_instrsSecond [0] instrsFirst(v0) -> null_instrsFirst [0] getWrite(v0) -> null_getWrite [0] getGotoSecond(v0) -> null_getGotoSecond [0] getGotoFirst(v0) -> null_getGotoFirst [0] getGoto(v0) -> null_getGoto [0] instrsConstrCheck(v0, v1) -> null_instrsConstrCheck [0] instrConstrCheck(v0, v1) -> null_instrConstrCheck [0] The TRS has the following type information: turing :: I:Empty:null_lookup:null_instrsSecond -> Cons:Nil:null_turing[Ite]:null_turing -> Cons:Nil:null_turing[Ite]:null_turing -> I:Empty:null_lookup:null_instrsSecond -> Cons:Nil:null_turing[Ite]:null_turing I :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> I:Empty:null_lookup:null_instrsSecond -> I:Empty:null_lookup:null_instrsSecond IfGoto :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst Cons :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> Cons:Nil:null_turing[Ite]:null_turing -> Cons:Nil:null_turing[Ite]:null_turing turing[Ite] :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck -> I:Empty:null_lookup:null_instrsSecond -> Cons:Nil:null_turing[Ite]:null_turing -> Cons:Nil:null_turing[Ite]:null_turing -> I:Empty:null_lookup:null_instrsSecond -> Cons:Nil:null_turing[Ite]:null_turing !EQ :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck Goto :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst lookup :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> I:Empty:null_lookup:null_instrsSecond -> I:Empty:null_lookup:null_instrsSecond Right :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst Nil :: Cons:Nil:null_turing[Ite]:null_turing 0 :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto Left :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst Write :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst Halt :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst Empty :: I:Empty:null_lookup:null_instrsSecond S :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto instrsConstrCheck :: I:Empty:null_lookup:null_instrsSecond -> I:Empty:null_lookup:null_instrsSecond -> True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck True :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck False :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck instrConstrCheck :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck notEmpty :: Cons:Nil:null_turing[Ite]:null_turing -> True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck instrsSecond :: I:Empty:null_lookup:null_instrsSecond -> I:Empty:null_lookup:null_instrsSecond instrsFirst :: I:Empty:null_lookup:null_instrsSecond -> IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst getWrite :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto getGotoSecond :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto getGotoFirst :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto getGoto :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst -> 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto run :: I:Empty:null_lookup:null_instrsSecond -> Cons:Nil:null_turing[Ite]:null_turing -> Cons:Nil:null_turing[Ite]:null_turing null_!EQ :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck null_turing[Ite] :: Cons:Nil:null_turing[Ite]:null_turing null_turing :: Cons:Nil:null_turing[Ite]:null_turing null_lookup :: I:Empty:null_lookup:null_instrsSecond null_notEmpty :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck null_instrsSecond :: I:Empty:null_lookup:null_instrsSecond null_instrsFirst :: IfGoto:Goto:Right:Left:Write:Halt:null_instrsFirst null_getWrite :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto null_getGotoSecond :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto null_getGotoFirst :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto null_getGoto :: 0:S:null_getWrite:null_getGotoSecond:null_getGotoFirst:null_getGoto null_instrsConstrCheck :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck null_instrConstrCheck :: True:False:null_!EQ:null_notEmpty:null_instrsConstrCheck:null_instrConstrCheck Rewrite Strategy: INNERMOST ---------------------------------------- (95) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: Right => 2 Nil => 0 0 => 0 Left => 1 Halt => 0 Empty => 0 True => 2 False => 1 null_!EQ => 0 null_turing[Ite] => 0 null_turing => 0 null_lookup => 0 null_notEmpty => 0 null_instrsSecond => 0 null_instrsFirst => 0 null_getWrite => 0 null_getGotoSecond => 0 null_getGotoFirst => 0 null_getGoto => 0 null_instrsConstrCheck => 0 null_instrConstrCheck => 0 ---------------------------------------- (96) Obligation: Complexity RNTS consisting of the following rules: !EQ(z, z') -{ 0 }-> 2 :|: z = 0, z' = 0 !EQ(z, z') -{ 0 }-> 1 :|: z' = 1 + y, y >= 0, z = 0 !EQ(z, z') -{ 0 }-> 1 :|: x >= 0, z = 1 + x, z' = 0 !EQ(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 !EQ(z, z') -{ 0 }-> !EQ(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x getGoto(z) -{ 1 }-> int :|: int >= 0, z = 1 + int getGoto(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 getGotoFirst(z) -{ 1 }-> i1 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoFirst(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 getGotoSecond(z) -{ 1 }-> i2 :|: z = 1 + i1 + i2, i1 >= 0, i2 >= 0 getGotoSecond(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 getWrite(z) -{ 1 }-> int :|: int >= 0, z = 1 + int getWrite(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat12 >= 0, igtNat22 >= 0, igtNat1 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1 + gtNat, z' = 1 + gtNat2, gtNat2 >= 0, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 2, z' = 2 instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 1, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 2 :|: wNat >= 0, z' = 1 + wNat2, wNat2 >= 0, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 1 + gtNat2, z = 1 + igtNat1 + igtNat2, gtNat2 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z' = 2, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, z' = 1 + wNat2, wNat2 >= 0, igtNat1 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat2 >= 0, z = 1 + igtNat1 + igtNat2, igtNat1 >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, igtNat12 >= 0, igtNat22 >= 0, gtNat >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, z' = 2, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, gtNat >= 0, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, z' = 1 + wNat2, wNat2 >= 0, gtNat >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1 + gtNat, gtNat >= 0, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 + gtNat2, gtNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 1 + wNat2, wNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 2, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, igtNat12 >= 0, igtNat22 >= 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + gtNat2, z = 1, gtNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 1 + wNat2, wNat2 >= 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z = 1, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, igtNat12 >= 0, igtNat22 >= 0, z = 1 + wNat, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z' = 1 + gtNat2, gtNat2 >= 0, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z' = 2, z = 1 + wNat instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z = 1 + wNat, z' = 1 instrConstrCheck(z, z') -{ 1 }-> 1 :|: wNat >= 0, z = 1 + wNat, z' = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: igtNat12 >= 0, igtNat22 >= 0, z = 0, z' = 1 + igtNat12 + igtNat22 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + gtNat2, gtNat2 >= 0, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 2, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1, z = 0 instrConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + wNat2, wNat2 >= 0, z = 0 instrConstrCheck(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: r1 >= 0, z' = 1 + x + y, x >= 0, y >= 0, l1 >= 0, z = 1 + l1 + r1 instrsConstrCheck(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: r1 >= 0, l1 >= 0, z = 1 + l1 + r1, z' = 0 instrsConstrCheck(z, z') -{ 1 }-> 1 :|: z' = 1 + x + y, x >= 0, y >= 0, z = 0 instrsConstrCheck(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 instrsFirst(z) -{ 1 }-> l :|: r >= 0, z = 1 + l + r, l >= 0 instrsFirst(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 instrsSecond(z) -{ 1 }-> r :|: r >= 0, z = 1 + l + r, l >= 0 instrsSecond(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 lookup(z, z') -{ 1 }-> instrs :|: instrs >= 0, z' = instrs, z = 0 lookup(z, z') -{ 1 }-> lookup(x, r) :|: r >= 0, x >= 0, z' = 1 + l + r, l >= 0, z = 1 + x lookup(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 notEmpty(z) -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0 notEmpty(z) -{ 1 }-> 1 :|: z = 0 notEmpty(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 run(z, z') -{ 1 }-> turing(prog, 0, tapeinput, prog) :|: tapeinput >= 0, z = prog, prog >= 0, z' = tapeinput turing(z, z', z'', z1) -{ 1 }-> rtape :|: r >= 0, z = 1 + 0 + r, prog >= 0, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape turing(z, z', z'', z1) -{ 1 }-> rtape :|: prog >= 0, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape, z = 0 turing(z, z', z'', z1) -{ 1 }-> turing[Ite](!EQ(x, i1), 1 + (1 + i1 + i2) + r, revltape, 1 + x + xs, prog) :|: r >= 0, xs >= 0, i1 >= 0, x >= 0, prog >= 0, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape, z = 1 + (1 + i1 + i2) + r, i2 >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, revltape, 1 + int + xs, prog) :|: r >= 0, xs >= 0, x >= 0, prog >= 0, z = 1 + (1 + int) + r, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape, int >= 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, xs, 1 + x + rtape, prog) :|: r >= 0, xs >= 0, z' = 1 + x + xs, x >= 0, prog >= 0, z1 = prog, rtape >= 0, z'' = rtape, z = 1 + 1 + r turing(z, z', z'', z1) -{ 1 }-> turing(r, 0, 1 + 0 + rtape, prog) :|: r >= 0, prog >= 0, z1 = prog, rtape >= 0, z'' = rtape, z = 1 + 1 + r, z' = 0 turing(z, z', z'', z1) -{ 1 }-> turing(r, 1 + x + revltape, xs, prog) :|: r >= 0, xs >= 0, x >= 0, prog >= 0, z = 1 + 2 + r, z1 = prog, z'' = 1 + x + xs, revltape >= 0, z' = revltape turing(z, z', z'', z1) -{ 1 }-> turing(r, 1 + 0 + revltape, 0, prog) :|: z'' = 0, r >= 0, prog >= 0, z = 1 + 2 + r, z1 = prog, revltape >= 0, z' = revltape turing(z, z', z'', z1) -{ 1 }-> turing(lookup(int, prog), revltape, rtape, prog) :|: r >= 0, prog >= 0, z = 1 + (1 + int) + r, z1 = prog, rtape >= 0, revltape >= 0, z' = revltape, z'' = rtape, int >= 0 turing(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(r, revltape, rtape, prog) :|: r >= 0, z = 1, z' = 1 + l + r, prog >= 0, l >= 0, z1 = rtape, rtape >= 0, revltape >= 0, z2 = prog, z'' = revltape turing[Ite](z, z', z'', z1, z2) -{ 0 }-> turing(lookup(i2, prog), revltape, rtape, prog) :|: z = 2, r >= 0, i1 >= 0, prog >= 0, z1 = rtape, rtape >= 0, revltape >= 0, z2 = prog, z'' = revltape, i2 >= 0, z' = 1 + (1 + i1 + i2) + r turing[Ite](z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (97) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True turing[Ite](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> turing(lookup(z1, z5), z3, z4, z5) turing[Ite](False, I(z0, z1), z2, z3, z4) -> turing(z1, z2, z3, z4) turing(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> turing[Ite](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) turing(I(Goto(z0), z1), z2, z3, z4) -> turing(lookup(z0, z4), z2, z3, z4) turing(I(Right, z0), z1, Cons(z2, z3), z4) -> turing(z0, Cons(z2, z1), z3, z4) turing(I(Right, z0), z1, Nil, z2) -> turing(z0, Cons(0, z1), Nil, z2) turing(I(Left, z0), Cons(z1, z2), z3, z4) -> turing(z0, z2, Cons(z1, z3), z4) turing(I(Left, z0), Nil, z1, z2) -> turing(z0, Nil, Cons(0, z1), z2) turing(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> turing(z1, z2, Cons(z0, z4), z5) turing(I(Halt, z0), z1, z2, z3) -> z2 turing(Empty, z0, z1, z2) -> z1 lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 instrsConstrCheck(I(z0, z1), I(z2, z3)) -> True instrsConstrCheck(I(z0, z1), Empty) -> False instrsConstrCheck(Empty, I(z0, z1)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(z0, z1), IfGoto(z2, z3)) -> True instrConstrCheck(IfGoto(z0, z1), Goto(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Right) -> False instrConstrCheck(IfGoto(z0, z1), Left) -> False instrConstrCheck(IfGoto(z0, z1), Write(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Halt) -> False instrConstrCheck(Goto(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Goto(z0), Goto(z1)) -> True instrConstrCheck(Goto(z0), Right) -> False instrConstrCheck(Goto(z0), Left) -> False instrConstrCheck(Goto(z0), Write(z1)) -> False instrConstrCheck(Goto(z0), Halt) -> False instrConstrCheck(Right, IfGoto(z0, z1)) -> False instrConstrCheck(Right, Goto(z0)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(z0)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(z0, z1)) -> False instrConstrCheck(Left, Goto(z0)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(z0)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Write(z0), Goto(z1)) -> False instrConstrCheck(Write(z0), Right) -> False instrConstrCheck(Write(z0), Left) -> False instrConstrCheck(Write(z0), Write(z1)) -> True instrConstrCheck(Write(z0), Halt) -> False instrConstrCheck(Halt, IfGoto(z0, z1)) -> False instrConstrCheck(Halt, Goto(z0)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(z0)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(z0, z1)) -> True notEmpty(Nil) -> False instrsSecond(I(z0, z1)) -> z1 instrsFirst(I(z0, z1)) -> z0 getWrite(Write(z0)) -> z0 getGotoSecond(IfGoto(z0, z1)) -> z1 getGotoFirst(IfGoto(z0, z1)) -> z0 getGoto(Goto(z0)) -> z0 run(z0, z1) -> turing(z0, Nil, z1, z0) Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) !EQ'(0, S(z0)) -> c1 !EQ'(S(z0), 0) -> c2 !EQ'(0, 0) -> c3 TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 INSTRSCONSTRCHECK(I(z0, z1), I(z2, z3)) -> c17 INSTRSCONSTRCHECK(I(z0, z1), Empty) -> c18 INSTRSCONSTRCHECK(Empty, I(z0, z1)) -> c19 INSTRSCONSTRCHECK(Empty, Empty) -> c20 INSTRCONSTRCHECK(IfGoto(z0, z1), IfGoto(z2, z3)) -> c21 INSTRCONSTRCHECK(IfGoto(z0, z1), Goto(z2)) -> c22 INSTRCONSTRCHECK(IfGoto(z0, z1), Right) -> c23 INSTRCONSTRCHECK(IfGoto(z0, z1), Left) -> c24 INSTRCONSTRCHECK(IfGoto(z0, z1), Write(z2)) -> c25 INSTRCONSTRCHECK(IfGoto(z0, z1), Halt) -> c26 INSTRCONSTRCHECK(Goto(z0), IfGoto(z1, z2)) -> c27 INSTRCONSTRCHECK(Goto(z0), Goto(z1)) -> c28 INSTRCONSTRCHECK(Goto(z0), Right) -> c29 INSTRCONSTRCHECK(Goto(z0), Left) -> c30 INSTRCONSTRCHECK(Goto(z0), Write(z1)) -> c31 INSTRCONSTRCHECK(Goto(z0), Halt) -> c32 INSTRCONSTRCHECK(Right, IfGoto(z0, z1)) -> c33 INSTRCONSTRCHECK(Right, Goto(z0)) -> c34 INSTRCONSTRCHECK(Right, Right) -> c35 INSTRCONSTRCHECK(Right, Left) -> c36 INSTRCONSTRCHECK(Right, Write(z0)) -> c37 INSTRCONSTRCHECK(Right, Halt) -> c38 INSTRCONSTRCHECK(Left, IfGoto(z0, z1)) -> c39 INSTRCONSTRCHECK(Left, Goto(z0)) -> c40 INSTRCONSTRCHECK(Left, Right) -> c41 INSTRCONSTRCHECK(Left, Left) -> c42 INSTRCONSTRCHECK(Left, Write(z0)) -> c43 INSTRCONSTRCHECK(Left, Halt) -> c44 INSTRCONSTRCHECK(Write(z0), IfGoto(z1, z2)) -> c45 INSTRCONSTRCHECK(Write(z0), Goto(z1)) -> c46 INSTRCONSTRCHECK(Write(z0), Right) -> c47 INSTRCONSTRCHECK(Write(z0), Left) -> c48 INSTRCONSTRCHECK(Write(z0), Write(z1)) -> c49 INSTRCONSTRCHECK(Write(z0), Halt) -> c50 INSTRCONSTRCHECK(Halt, IfGoto(z0, z1)) -> c51 INSTRCONSTRCHECK(Halt, Goto(z0)) -> c52 INSTRCONSTRCHECK(Halt, Right) -> c53 INSTRCONSTRCHECK(Halt, Left) -> c54 INSTRCONSTRCHECK(Halt, Write(z0)) -> c55 INSTRCONSTRCHECK(Halt, Halt) -> c56 NOTEMPTY(Cons(z0, z1)) -> c57 NOTEMPTY(Nil) -> c58 INSTRSSECOND(I(z0, z1)) -> c59 INSTRSFIRST(I(z0, z1)) -> c60 GETWRITE(Write(z0)) -> c61 GETGOTOSECOND(IfGoto(z0, z1)) -> c62 GETGOTOFIRST(IfGoto(z0, z1)) -> c63 GETGOTO(Goto(z0)) -> c64 RUN(z0, z1) -> c65(TURING(z0, Nil, z1, z0)) S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 INSTRSCONSTRCHECK(I(z0, z1), I(z2, z3)) -> c17 INSTRSCONSTRCHECK(I(z0, z1), Empty) -> c18 INSTRSCONSTRCHECK(Empty, I(z0, z1)) -> c19 INSTRSCONSTRCHECK(Empty, Empty) -> c20 INSTRCONSTRCHECK(IfGoto(z0, z1), IfGoto(z2, z3)) -> c21 INSTRCONSTRCHECK(IfGoto(z0, z1), Goto(z2)) -> c22 INSTRCONSTRCHECK(IfGoto(z0, z1), Right) -> c23 INSTRCONSTRCHECK(IfGoto(z0, z1), Left) -> c24 INSTRCONSTRCHECK(IfGoto(z0, z1), Write(z2)) -> c25 INSTRCONSTRCHECK(IfGoto(z0, z1), Halt) -> c26 INSTRCONSTRCHECK(Goto(z0), IfGoto(z1, z2)) -> c27 INSTRCONSTRCHECK(Goto(z0), Goto(z1)) -> c28 INSTRCONSTRCHECK(Goto(z0), Right) -> c29 INSTRCONSTRCHECK(Goto(z0), Left) -> c30 INSTRCONSTRCHECK(Goto(z0), Write(z1)) -> c31 INSTRCONSTRCHECK(Goto(z0), Halt) -> c32 INSTRCONSTRCHECK(Right, IfGoto(z0, z1)) -> c33 INSTRCONSTRCHECK(Right, Goto(z0)) -> c34 INSTRCONSTRCHECK(Right, Right) -> c35 INSTRCONSTRCHECK(Right, Left) -> c36 INSTRCONSTRCHECK(Right, Write(z0)) -> c37 INSTRCONSTRCHECK(Right, Halt) -> c38 INSTRCONSTRCHECK(Left, IfGoto(z0, z1)) -> c39 INSTRCONSTRCHECK(Left, Goto(z0)) -> c40 INSTRCONSTRCHECK(Left, Right) -> c41 INSTRCONSTRCHECK(Left, Left) -> c42 INSTRCONSTRCHECK(Left, Write(z0)) -> c43 INSTRCONSTRCHECK(Left, Halt) -> c44 INSTRCONSTRCHECK(Write(z0), IfGoto(z1, z2)) -> c45 INSTRCONSTRCHECK(Write(z0), Goto(z1)) -> c46 INSTRCONSTRCHECK(Write(z0), Right) -> c47 INSTRCONSTRCHECK(Write(z0), Left) -> c48 INSTRCONSTRCHECK(Write(z0), Write(z1)) -> c49 INSTRCONSTRCHECK(Write(z0), Halt) -> c50 INSTRCONSTRCHECK(Halt, IfGoto(z0, z1)) -> c51 INSTRCONSTRCHECK(Halt, Goto(z0)) -> c52 INSTRCONSTRCHECK(Halt, Right) -> c53 INSTRCONSTRCHECK(Halt, Left) -> c54 INSTRCONSTRCHECK(Halt, Write(z0)) -> c55 INSTRCONSTRCHECK(Halt, Halt) -> c56 NOTEMPTY(Cons(z0, z1)) -> c57 NOTEMPTY(Nil) -> c58 INSTRSSECOND(I(z0, z1)) -> c59 INSTRSFIRST(I(z0, z1)) -> c60 GETWRITE(Write(z0)) -> c61 GETGOTOSECOND(IfGoto(z0, z1)) -> c62 GETGOTOFIRST(IfGoto(z0, z1)) -> c63 GETGOTO(Goto(z0)) -> c64 RUN(z0, z1) -> c65(TURING(z0, Nil, z1, z0)) K tuples:none Defined Rule Symbols: turing_4, lookup_2, instrsConstrCheck_2, instrConstrCheck_2, notEmpty_1, instrsSecond_1, instrsFirst_1, getWrite_1, getGotoSecond_1, getGotoFirst_1, getGoto_1, run_2, !EQ_2, turing[Ite]_5 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2, INSTRSCONSTRCHECK_2, INSTRCONSTRCHECK_2, NOTEMPTY_1, INSTRSSECOND_1, INSTRSFIRST_1, GETWRITE_1, GETGOTOSECOND_1, GETGOTOFIRST_1, GETGOTO_1, RUN_2 Compound Symbols: c_1, c1, c2, c3, c4_2, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c13, c14, c15_1, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65_1 ---------------------------------------- (99) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: RUN(z0, z1) -> c65(TURING(z0, Nil, z1, z0)) Removed 51 trailing nodes: INSTRCONSTRCHECK(Halt, Halt) -> c56 INSTRCONSTRCHECK(Write(z0), Halt) -> c50 INSTRCONSTRCHECK(Goto(z0), Halt) -> c32 !EQ'(S(z0), 0) -> c2 INSTRCONSTRCHECK(IfGoto(z0, z1), IfGoto(z2, z3)) -> c21 INSTRCONSTRCHECK(Write(z0), IfGoto(z1, z2)) -> c45 INSTRCONSTRCHECK(Right, Halt) -> c38 INSTRCONSTRCHECK(IfGoto(z0, z1), Left) -> c24 INSTRCONSTRCHECK(Goto(z0), Right) -> c29 INSTRCONSTRCHECK(Left, IfGoto(z0, z1)) -> c39 INSTRCONSTRCHECK(Goto(z0), Goto(z1)) -> c28 INSTRCONSTRCHECK(Goto(z0), Left) -> c30 GETWRITE(Write(z0)) -> c61 INSTRCONSTRCHECK(Halt, Left) -> c54 INSTRCONSTRCHECK(Goto(z0), IfGoto(z1, z2)) -> c27 INSTRSCONSTRCHECK(I(z0, z1), Empty) -> c18 GETGOTOFIRST(IfGoto(z0, z1)) -> c63 INSTRCONSTRCHECK(Right, Goto(z0)) -> c34 INSTRCONSTRCHECK(Halt, IfGoto(z0, z1)) -> c51 INSTRCONSTRCHECK(Left, Goto(z0)) -> c40 INSTRCONSTRCHECK(IfGoto(z0, z1), Goto(z2)) -> c22 INSTRCONSTRCHECK(Write(z0), Right) -> c47 INSTRCONSTRCHECK(IfGoto(z0, z1), Write(z2)) -> c25 INSTRCONSTRCHECK(Halt, Write(z0)) -> c55 INSTRCONSTRCHECK(Right, Right) -> c35 INSTRCONSTRCHECK(Write(z0), Write(z1)) -> c49 INSTRCONSTRCHECK(Write(z0), Goto(z1)) -> c46 GETGOTO(Goto(z0)) -> c64 INSTRSCONSTRCHECK(Empty, I(z0, z1)) -> c19 INSTRCONSTRCHECK(Right, Write(z0)) -> c37 GETGOTOSECOND(IfGoto(z0, z1)) -> c62 INSTRCONSTRCHECK(IfGoto(z0, z1), Halt) -> c26 INSTRSSECOND(I(z0, z1)) -> c59 INSTRCONSTRCHECK(Halt, Right) -> c53 INSTRCONSTRCHECK(Left, Write(z0)) -> c43 INSTRCONSTRCHECK(Halt, Goto(z0)) -> c52 INSTRSFIRST(I(z0, z1)) -> c60 !EQ'(0, 0) -> c3 INSTRCONSTRCHECK(IfGoto(z0, z1), Right) -> c23 INSTRCONSTRCHECK(Right, Left) -> c36 !EQ'(0, S(z0)) -> c1 INSTRCONSTRCHECK(Left, Left) -> c42 INSTRCONSTRCHECK(Write(z0), Left) -> c48 INSTRSCONSTRCHECK(Empty, Empty) -> c20 INSTRCONSTRCHECK(Left, Right) -> c41 NOTEMPTY(Nil) -> c58 NOTEMPTY(Cons(z0, z1)) -> c57 INSTRCONSTRCHECK(Left, Halt) -> c44 INSTRSCONSTRCHECK(I(z0, z1), I(z2, z3)) -> c17 INSTRCONSTRCHECK(Right, IfGoto(z0, z1)) -> c33 INSTRCONSTRCHECK(Goto(z0), Write(z1)) -> c31 ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True turing[Ite](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> turing(lookup(z1, z5), z3, z4, z5) turing[Ite](False, I(z0, z1), z2, z3, z4) -> turing(z1, z2, z3, z4) turing(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> turing[Ite](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) turing(I(Goto(z0), z1), z2, z3, z4) -> turing(lookup(z0, z4), z2, z3, z4) turing(I(Right, z0), z1, Cons(z2, z3), z4) -> turing(z0, Cons(z2, z1), z3, z4) turing(I(Right, z0), z1, Nil, z2) -> turing(z0, Cons(0, z1), Nil, z2) turing(I(Left, z0), Cons(z1, z2), z3, z4) -> turing(z0, z2, Cons(z1, z3), z4) turing(I(Left, z0), Nil, z1, z2) -> turing(z0, Nil, Cons(0, z1), z2) turing(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> turing(z1, z2, Cons(z0, z4), z5) turing(I(Halt, z0), z1, z2, z3) -> z2 turing(Empty, z0, z1, z2) -> z1 lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 instrsConstrCheck(I(z0, z1), I(z2, z3)) -> True instrsConstrCheck(I(z0, z1), Empty) -> False instrsConstrCheck(Empty, I(z0, z1)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(z0, z1), IfGoto(z2, z3)) -> True instrConstrCheck(IfGoto(z0, z1), Goto(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Right) -> False instrConstrCheck(IfGoto(z0, z1), Left) -> False instrConstrCheck(IfGoto(z0, z1), Write(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Halt) -> False instrConstrCheck(Goto(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Goto(z0), Goto(z1)) -> True instrConstrCheck(Goto(z0), Right) -> False instrConstrCheck(Goto(z0), Left) -> False instrConstrCheck(Goto(z0), Write(z1)) -> False instrConstrCheck(Goto(z0), Halt) -> False instrConstrCheck(Right, IfGoto(z0, z1)) -> False instrConstrCheck(Right, Goto(z0)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(z0)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(z0, z1)) -> False instrConstrCheck(Left, Goto(z0)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(z0)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Write(z0), Goto(z1)) -> False instrConstrCheck(Write(z0), Right) -> False instrConstrCheck(Write(z0), Left) -> False instrConstrCheck(Write(z0), Write(z1)) -> True instrConstrCheck(Write(z0), Halt) -> False instrConstrCheck(Halt, IfGoto(z0, z1)) -> False instrConstrCheck(Halt, Goto(z0)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(z0)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(z0, z1)) -> True notEmpty(Nil) -> False instrsSecond(I(z0, z1)) -> z1 instrsFirst(I(z0, z1)) -> z0 getWrite(Write(z0)) -> z0 getGotoSecond(IfGoto(z0, z1)) -> z1 getGotoFirst(IfGoto(z0, z1)) -> z0 getGoto(Goto(z0)) -> z0 run(z0, z1) -> turing(z0, Nil, z1, z0) Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 K tuples:none Defined Rule Symbols: turing_4, lookup_2, instrsConstrCheck_2, instrConstrCheck_2, notEmpty_1, instrsSecond_1, instrsFirst_1, getWrite_1, getGotoSecond_1, getGotoFirst_1, getGoto_1, run_2, !EQ_2, turing[Ite]_5 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c4_2, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c13, c14, c15_1, c16 ---------------------------------------- (101) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: turing[Ite](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> turing(lookup(z1, z5), z3, z4, z5) turing[Ite](False, I(z0, z1), z2, z3, z4) -> turing(z1, z2, z3, z4) turing(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> turing[Ite](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) turing(I(Goto(z0), z1), z2, z3, z4) -> turing(lookup(z0, z4), z2, z3, z4) turing(I(Right, z0), z1, Cons(z2, z3), z4) -> turing(z0, Cons(z2, z1), z3, z4) turing(I(Right, z0), z1, Nil, z2) -> turing(z0, Cons(0, z1), Nil, z2) turing(I(Left, z0), Cons(z1, z2), z3, z4) -> turing(z0, z2, Cons(z1, z3), z4) turing(I(Left, z0), Nil, z1, z2) -> turing(z0, Nil, Cons(0, z1), z2) turing(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> turing(z1, z2, Cons(z0, z4), z5) turing(I(Halt, z0), z1, z2, z3) -> z2 turing(Empty, z0, z1, z2) -> z1 instrsConstrCheck(I(z0, z1), I(z2, z3)) -> True instrsConstrCheck(I(z0, z1), Empty) -> False instrsConstrCheck(Empty, I(z0, z1)) -> False instrsConstrCheck(Empty, Empty) -> True instrConstrCheck(IfGoto(z0, z1), IfGoto(z2, z3)) -> True instrConstrCheck(IfGoto(z0, z1), Goto(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Right) -> False instrConstrCheck(IfGoto(z0, z1), Left) -> False instrConstrCheck(IfGoto(z0, z1), Write(z2)) -> False instrConstrCheck(IfGoto(z0, z1), Halt) -> False instrConstrCheck(Goto(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Goto(z0), Goto(z1)) -> True instrConstrCheck(Goto(z0), Right) -> False instrConstrCheck(Goto(z0), Left) -> False instrConstrCheck(Goto(z0), Write(z1)) -> False instrConstrCheck(Goto(z0), Halt) -> False instrConstrCheck(Right, IfGoto(z0, z1)) -> False instrConstrCheck(Right, Goto(z0)) -> False instrConstrCheck(Right, Right) -> True instrConstrCheck(Right, Left) -> False instrConstrCheck(Right, Write(z0)) -> False instrConstrCheck(Right, Halt) -> False instrConstrCheck(Left, IfGoto(z0, z1)) -> False instrConstrCheck(Left, Goto(z0)) -> False instrConstrCheck(Left, Right) -> False instrConstrCheck(Left, Left) -> True instrConstrCheck(Left, Write(z0)) -> False instrConstrCheck(Left, Halt) -> False instrConstrCheck(Write(z0), IfGoto(z1, z2)) -> False instrConstrCheck(Write(z0), Goto(z1)) -> False instrConstrCheck(Write(z0), Right) -> False instrConstrCheck(Write(z0), Left) -> False instrConstrCheck(Write(z0), Write(z1)) -> True instrConstrCheck(Write(z0), Halt) -> False instrConstrCheck(Halt, IfGoto(z0, z1)) -> False instrConstrCheck(Halt, Goto(z0)) -> False instrConstrCheck(Halt, Right) -> False instrConstrCheck(Halt, Left) -> False instrConstrCheck(Halt, Write(z0)) -> False instrConstrCheck(Halt, Halt) -> True notEmpty(Cons(z0, z1)) -> True notEmpty(Nil) -> False instrsSecond(I(z0, z1)) -> z1 instrsFirst(I(z0, z1)) -> z0 getWrite(Write(z0)) -> z0 getGotoSecond(IfGoto(z0, z1)) -> z1 getGotoFirst(IfGoto(z0, z1)) -> z0 getGoto(Goto(z0)) -> z0 run(z0, z1) -> turing(z0, Nil, z1, z0) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c4_2, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c13, c14, c15_1, c16 ---------------------------------------- (103) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 We considered the (Usable) Rules:none And the Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 The order we found is given by the following interpretation: Polynomial interpretation : POL(!EQ(x_1, x_2)) = [2]x_2 POL(!EQ'(x_1, x_2)) = 0 POL(0) = 0 POL(Cons(x_1, x_2)) = 0 POL(Empty) = 0 POL(False) = 0 POL(Goto(x_1)) = 0 POL(Halt) = 0 POL(I(x_1, x_2)) = [1] POL(IfGoto(x_1, x_2)) = 0 POL(LOOKUP(x_1, x_2)) = 0 POL(Left) = 0 POL(Nil) = 0 POL(Right) = 0 POL(S(x_1)) = [1] + x_1 POL(TURING(x_1, x_2, x_3, x_4)) = [1] POL(TURING[ITE](x_1, x_2, x_3, x_4, x_5)) = x_2^2 POL(True) = 0 POL(Write(x_1)) = 0 POL(c(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13) = 0 POL(c14) = 0 POL(c15(x_1)) = x_1 POL(c16) = 0 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1, x_2)) = x_1 + x_2 POL(c7(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(lookup(x_1, x_2)) = x_2^2 ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 K tuples: TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c4_2, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c13, c14, c15_1, c16 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING[ITE](True, I(IfGoto(z0, z1), z2), z3, z4, z5) -> c4(TURING(lookup(z1, z5), z3, z4, z5), LOOKUP(z1, z5)) by TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 K tuples: TURING(I(Halt, z0), z1, z2, z3) -> c13 TURING(Empty, z0, z1, z2) -> c14 Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c13, c14, c15_1, c16, c4_2 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing nodes: TURING(Empty, z0, z1, z2) -> c14 TURING(I(Halt, z0), z1, z2, z3) -> c13 ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) S tuples: TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c6_2, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING(I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6) -> c6(TURING[ITE](!EQ(z4, z0), I(IfGoto(z0, z1), z2), z3, Cons(z4, z5), z6), !EQ'(z4, z0)) by TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6), !EQ'(0, S(z0))) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), 0)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6), !EQ'(0, 0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6), !EQ'(0, S(z0))) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), 0)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6), !EQ'(0, 0)) S tuples: TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6), !EQ'(0, S(z0))) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), 0)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6), !EQ'(0, 0)) K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_2 ---------------------------------------- (111) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) S tuples: TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c7_2, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_2, c6_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING(I(Goto(z0), z1), z2, z3, z4) -> c7(TURING(lookup(z0, z4), z2, z3, z4), LOOKUP(z0, z4)) by TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_2, c6_1, c7_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING[ITE](True, I(IfGoto(x0, S(z0)), x2), x3, x4, I(z1, z2)) -> c4(TURING(lookup(z0, z2), x3, x4, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) by TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_2, c6_1, c7_2, c4_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING(I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(z1), x1), x2), x3, Cons(S(z0), x5), x6), !EQ'(S(z0), S(z1))) by TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) K tuples:none Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2 ---------------------------------------- (119) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) We considered the (Usable) Rules:none And the Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) The order we found is given by the following interpretation: Polynomial interpretation : POL(!EQ(x_1, x_2)) = [3] POL(!EQ'(x_1, x_2)) = 0 POL(0) = 0 POL(Cons(x_1, x_2)) = [3] + x_2 POL(False) = [3] POL(Goto(x_1)) = 0 POL(I(x_1, x_2)) = [1] POL(IfGoto(x_1, x_2)) = [3] + x_2 POL(LOOKUP(x_1, x_2)) = 0 POL(Left) = 0 POL(Nil) = 0 POL(Right) = 0 POL(S(x_1)) = x_1 POL(TURING(x_1, x_2, x_3, x_4)) = [1] POL(TURING[ITE](x_1, x_2, x_3, x_4, x_5)) = x_2 POL(True) = [3] POL(Write(x_1)) = 0 POL(c(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16) = 0 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c6(x_1, x_2)) = x_1 + x_2 POL(c7(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(lookup(x_1, x_2)) = [3]x_1 + [3]x_2 ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace TURING(I(Goto(S(z0)), x1), x2, x3, I(z1, z2)) -> c7(TURING(lookup(z0, z2), x2, x3, I(z1, z2)), LOOKUP(S(z0), I(z1, z2))) by TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1 ---------------------------------------- (123) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) We considered the (Usable) Rules:none And the Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) The order we found is given by the following interpretation: Polynomial interpretation : POL(!EQ(x_1, x_2)) = [1] + x_1 + x_2 POL(!EQ'(x_1, x_2)) = 0 POL(0) = [1] POL(Cons(x_1, x_2)) = x_2 POL(False) = [1] POL(Goto(x_1)) = 0 POL(I(x_1, x_2)) = [1] + x_1 + x_2 POL(IfGoto(x_1, x_2)) = [1] + x_1 + x_2 POL(LOOKUP(x_1, x_2)) = 0 POL(Left) = 0 POL(Nil) = 0 POL(Right) = 0 POL(S(x_1)) = [1] + x_1 POL(TURING(x_1, x_2, x_3, x_4)) = x_2 + x_3 + x_4 POL(TURING[ITE](x_1, x_2, x_3, x_4, x_5)) = x_3 + x_4 + x_5 POL(True) = [1] POL(Write(x_1)) = 0 POL(c(x_1)) = x_1 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16) = 0 POL(c4(x_1)) = x_1 POL(c4(x_1, x_2)) = x_1 + x_2 POL(c5(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c6(x_1, x_2)) = x_1 + x_2 POL(c7(x_1)) = x_1 POL(c7(x_1, x_2)) = x_1 + x_2 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(lookup(x_1, x_2)) = x_1 + x_2 ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: !EQ'_2, TURING[ITE]_5, TURING_4, LOOKUP_2 Compound Symbols: c_1, c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1 ---------------------------------------- (125) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace !EQ'(S(z0), S(z1)) -> c(!EQ'(z0, z1)) by !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(S(z0)))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(0))) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6), !EQ'(S(0), S(0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING[ITE]_5, TURING_4, LOOKUP_2, !EQ'_2 Compound Symbols: c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1, c_1 ---------------------------------------- (127) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING[ITE]_5, TURING_4, LOOKUP_2, !EQ'_2 Compound Symbols: c5_1, c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1, c_1 ---------------------------------------- (129) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING[ITE](False, I(z0, z1), z2, z3, z4) -> c5(TURING(z1, z2, z3, z4)) by TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1, c_1, c5_1 ---------------------------------------- (131) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Right, z0), z1, Nil, z2) -> c9(TURING(z0, Cons(0, z1), Nil, z2)) by TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c8_1, c10_1, c11_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1, c_1, c5_1, c9_1 ---------------------------------------- (133) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Left, z0), Nil, z1, z2) -> c11(TURING(z0, Nil, Cons(0, z1), z2)) by TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c8_1, c10_1, c12_1, c15_1, c16, c4_2, c6_1, c7_2, c4_1, c6_2, c7_1, c_1, c5_1, c9_1, c11_1 ---------------------------------------- (135) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING[ITE](True, I(IfGoto(x0, 0), x2), x3, x4, z0) -> c4(TURING(z0, x3, x4, z0), LOOKUP(0, z0)) by TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) S tuples: TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c8_1, c10_1, c12_1, c15_1, c16, c6_1, c7_2, c4_2, c4_1, c6_2, c7_1, c_1, c5_1, c9_1, c11_1 ---------------------------------------- (137) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(Right, z0), z1, Cons(z2, z3), z4) -> c8(TURING(z0, Cons(z2, z1), z3, z4)) by TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) S tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c10_1, c12_1, c15_1, c16, c6_1, c7_2, c4_2, c4_1, c6_2, c7_1, c_1, c5_1, c9_1, c11_1, c8_1 ---------------------------------------- (139) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Goto(0), x1), x2, x3, z0) -> c7(TURING(z0, x2, x3, z0), LOOKUP(0, z0)) by TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) S tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c10_1, c12_1, c15_1, c16, c6_1, c4_2, c4_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c8_1 ---------------------------------------- (141) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING[ITE](True, I(IfGoto(x0, S(S(z0))), x2), x3, x4, I(x5, I(z1, z2))) -> c4(TURING(lookup(z0, z2), x3, x4, I(x5, I(z1, z2))), LOOKUP(S(S(z0)), I(x5, I(z1, z2)))) by TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) S tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c10_1, c12_1, c15_1, c16, c6_1, c4_2, c4_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c8_1 ---------------------------------------- (143) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING[ITE](True, I(IfGoto(x0, S(0)), x2), x3, x4, I(x5, z0)) -> c4(TURING(z0, x3, x4, I(x5, z0)), LOOKUP(S(0), I(x5, z0))) by TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) S tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, TURING[ITE]_5, !EQ'_2 Compound Symbols: c10_1, c12_1, c15_1, c16, c6_1, c4_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c4_2, c8_1 ---------------------------------------- (145) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING[ITE](True, I(IfGoto(x0, S(x1)), x2), x3, x4, I(x5, x6)) -> c4(LOOKUP(S(x1), I(x5, x6))) by TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) S tuples: TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c10_1, c12_1, c15_1, c16, c6_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1 ---------------------------------------- (147) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(Left, z0), Cons(z1, z2), z3, z4) -> c10(TURING(z0, z2, Cons(z1, z3), z4)) by TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) S tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c12_1, c15_1, c16, c6_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1 ---------------------------------------- (149) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Goto(S(0)), x1), x2, x3, I(x4, z0)) -> c7(TURING(z0, x2, x3, I(x4, z0)), LOOKUP(S(0), I(x4, z0))) by TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) S tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c12_1, c15_1, c16, c6_1, c6_2, c7_2, c7_1, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1 ---------------------------------------- (151) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Goto(S(x0)), x1), x2, x3, I(x4, x5)) -> c7(LOOKUP(S(x0), I(x4, x5))) by TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) S tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c12_1, c15_1, c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1 ---------------------------------------- (153) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Right, z0), x2, Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, x2), Nil, I(Right, z0))) by TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) S tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c12_1, c15_1, c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1 ---------------------------------------- (155) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace TURING(I(Left, z0), Nil, x3, I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, x3), I(Left, z0))) by TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) S tuples: TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: TURING_4, LOOKUP_2, !EQ'_2, TURING[ITE]_5 Compound Symbols: c12_1, c15_1, c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1 ---------------------------------------- (157) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(Write(z0), z1), z2, Cons(z3, z4), z5) -> c12(TURING(z1, z2, Cons(z0, z4), z5)) by TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) S tuples: LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, !EQ'_2, TURING[ITE]_5 Compound Symbols: c15_1, c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1 ---------------------------------------- (159) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace LOOKUP(S(z0), I(z1, z2)) -> c15(LOOKUP(z0, z2)) by LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, !EQ'_2, TURING[ITE]_5 Compound Symbols: c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1 ---------------------------------------- (161) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](True, I(IfGoto(0, x1), x2), x3, Cons(0, x5), x6)) by TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) K tuples: TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, !EQ'_2, TURING[ITE]_5 Compound Symbols: c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(IfGoto(S(x0), x1), x2), x3, Cons(S(x4), x5), x6) -> c6(!EQ'(S(x4), S(x0))) by TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, !EQ'_2, TURING[ITE]_5 Compound Symbols: c16, c6_1, c6_2, c7_2, c_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1 ---------------------------------------- (165) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace !EQ'(S(S(y0)), S(S(y1))) -> c(!EQ'(S(y0), S(y1))) by !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_1, c6_2, c7_2, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](True, I(IfGoto(S(0), x1), x2), x3, Cons(S(0), x5), x6)) by TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_1, c6_2, c7_2, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (169) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING[ITE](False, I(IfGoto(S(x0), x1), x2), x3, Cons(0, x4), x5) -> c5(TURING(x2, x3, Cons(0, x4), x5)) by TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(S(y0), y1), y2), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(y1, y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y1), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y1)), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(0, z4), I(Left, y3)) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(0, z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(0, z4), I(y3, I(Left, y4))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(0, z4), I(y3, I(Left, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, 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I(Goto(S(S(y1))), y2)))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(S(y1))), y2))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(0)), y1)))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(y1)), y2)))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(0, Cons(S(0), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(0, Cons(S(S(y5)), 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I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(y2, y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(y2, y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(0, y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(y2), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y2), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(0), y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Write(y1), y2)))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3)))), Cons(0, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(0, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(0, y1), y2)))), Cons(S(y3), y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(0, y1), y2))), Cons(S(y3), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(0, y1), y2)))), Cons(0, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(0, y1), y2))), Cons(0, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3)))), Cons(S(y4), y5), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(S(S(y1))), y2)))), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(S(0)), y1)))), Cons(y2, y3), Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(S(0)), y1))), Cons(y2, y3), Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(S(y1)), y2)))), Cons(y3, y4), Cons(0, z4), I(y7, y8)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(y7, y8))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3)))), Cons(S(0), y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(0), y1), y2)))), Cons(S(S(y3)), y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(S(y3)), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(0), y1), y2)))), Cons(S(0), y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(0), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Nil), Cons(0, z4), I(Left, y5)) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(0, z4), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Nil), Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Nil), Cons(0, z4), I(y5, I(Left, y6))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(0, z4), I(y5, I(Left, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(S(y2), Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(S(y2), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(S(S(y2)), Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(S(S(y2)), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(S(0), Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(S(0), Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Right, I(Right, y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Right, I(Right, y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Right, I(Left, y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Right, I(Left, y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Right, I(Write(y1), y2))))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Right, I(Write(y1), y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2))))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Left, I(Right, I(IfGoto(0, y1), y2))))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Left, I(Right, I(IfGoto(0, y1), y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Right, I(Goto(0), y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Right, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(0, z4), z5) -> 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I(Left, I(Right, I(Goto(S(y1)), y2)))), Cons(y3, y4), Cons(0, z4), I(y7, y8))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(Right, I(IfGoto(S(0), y1), y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), z5)) 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y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, 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I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(S(y1))), y2)), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(y7, y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(y7, y8))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), I(y2, y3)))), z3, Cons(0, z4), I(Goto(S(y7)), I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(y2, y3))), z3, Cons(0, z4), I(Goto(S(y7)), I(y8, y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2)))), z3, Cons(0, z4), I(Goto(S(y6)), I(Goto(0), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(S(y6)), I(Goto(0), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), I(y1, y2)))), Nil, Cons(0, z4), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1))))), Nil, Cons(0, z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(0, z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(Goto(S(y7)), y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(Goto(S(y7)), y8))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(y1, y2)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, I(y1, y2))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, z4), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y0))), Nil, Cons(0, z4), I(Left, y3)) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(0, z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(y2, y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(y2, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(0, y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(0, y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y0, y1)))), Nil, Cons(0, z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(0, z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(y2), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(y2), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(0), y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(0), y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y0)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y0))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, I(y1, y2)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(y1, y2))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y0, y1)))), Nil, Cons(0, z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(0, z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Nil, Cons(0, z4), I(Left, I(Left, y4))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Nil, Cons(0, z4), I(Left, I(Left, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(0, 0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(0, S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y0)), z3, Cons(0, z4), I(y3, y4)) -> c5(TURING(I(IfGoto(0, S(0)), y0), z3, Cons(0, z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y0)), y1)), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(IfGoto(0, S(y0)), y1), z3, Cons(0, z4), I(y4, y5))) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(S(y0), y1), y2), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(y1, y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y1), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y1)), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), 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I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y0))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Left, y1)))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Right, I(Left, y1))), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Write(y1), y2)))), z3, Cons(0, Cons(y5, y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(Write(y1), y2))), z3, Cons(0, Cons(y5, y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(0, Cons(0, y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(0, Cons(0, y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(0), y1)))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Right, I(Goto(0), y1))), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(S(y1))), y2)))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(S(y1))), y2))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(0)), y1)))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(y1)), y2)))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(0, Cons(S(0), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Right, I(Right, y0)))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Write(0), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(Right, y4)) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(Right, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(y2, y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(y2, y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(0, y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(y2), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y2), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(0), y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Write(y1), y2)))), Cons(y3, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3)))), Cons(0, y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(0, y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(0, y1), y2)))), Cons(S(y3), y4), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(0, y1), y2))), Cons(S(y3), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(0, y1), y2)))), Cons(0, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(0, y1), y2))), Cons(0, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3)))), Cons(S(y4), y5), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(S(S(y1))), y2)))), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(0, z4), I(y7, I(y8, y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(S(0)), y1)))), Cons(y2, y3), Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(S(0)), y1))), Cons(y2, y3), Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), 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I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(Goto(S(y7)), y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(Goto(S(y7)), y8))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(y1, y2)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, I(y1, y2))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, z4), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(0, z4), I(Left, y4)) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(0, z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y0))), Nil, Cons(0, z4), I(Left, y3)) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(0, z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(y2, y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(y2, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(0, y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(0, y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y0, y1)))), Nil, Cons(0, z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(0, z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(y2), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(y2), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, Cons(S(0), y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, Cons(S(0), y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y0)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y0))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, I(y1, y2)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(y1, y2))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y0, y1)))), Nil, Cons(0, z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(0, z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Nil, Cons(0, z4), I(Left, I(Left, y4))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Nil, Cons(0, z4), I(Left, I(Left, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(0, 0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(0, S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y0)), z3, Cons(0, z4), I(y3, y4)) -> c5(TURING(I(IfGoto(0, S(0)), y0), z3, Cons(0, z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y0)), y1)), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(IfGoto(0, S(y0)), y1), z3, Cons(0, z4), I(y4, y5))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_1, c6_2, c7_2, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(z0), x1), x2), x3, Cons(0, x5), x6)) by TURING(I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Cons(y4, y5)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), 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Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(S(y0), y1), y2), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(y1, y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Goto(0), 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Cons(0, z4), I(Left, I(Left, y3))) -> c5(TURING(I(Left, I(Left, y0)), Nil, Cons(0, z4), I(Left, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Write(y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Write(y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(S(y0), y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(IfGoto(0, y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(IfGoto(0, y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(0, y0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(IfGoto(0, y0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(S(y1)), y2), y3)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(IfGoto(S(y1), y2), y3))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(IfGoto(S(y1), y2), y3)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(S(y1))), y2))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Goto(S(S(y1))), y2)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Left, y1))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, 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c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(0), y1)))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Right, I(Goto(0), y1))), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(S(y1))), y2)))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(S(y1))), y2))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(0)), y1)))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Goto(S(y1)), y2)))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(0, Cons(S(0), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Right, I(Right, y0)))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Write(0), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(Right, y4)) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(Right, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(y2, y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(y2, y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(0, y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(y2), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y2), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(0, Cons(S(0), y2)), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(0, z4), I(Goto(0), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Left, y1)))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), 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c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(0, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(0, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(S(y3)), y4), y5)))), Cons(S(S(y6)), y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, 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Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, 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TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(IfGoto(S(0), y3), y4)))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(IfGoto(S(0), y3), y4)))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(IfGoto(S(0), y3), y4)))), z3, Cons(0, Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(IfGoto(S(0), y3), y4)))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Right, I(Right, y2)))), z3, Cons(0, Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Right, I(Right, y2)))), z3, Cons(0, Nil), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(Right, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(Right, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(y5, I(Right, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Nil), I(y5, I(Right, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(y6, I(Goto(0), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), z3, Cons(0, z4), I(y6, I(Goto(0), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(0), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(0), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(y3, y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(0, y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(y3), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(0, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(0, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(S(y3)), y4), y5)))), Cons(S(S(y6)), y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(S(y3)), y4), y5)))), Cons(S(S(y6)), y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(S(y6), y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(S(y6), y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(S(y3))), y4)))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(S(y3))), y4)))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(0)), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(0)), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(y3)), y4)))), Cons(y5, y6), Cons(0, z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(S(y3)), y4)))), Cons(y5, y6), Cons(0, z4), I(y8, y9))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(S(y3)), y4), y5)))), Cons(S(0), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(S(y3)), y4), y5)))), Cons(S(0), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(0), y3), y4)))), Cons(S(S(y5)), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(0), y3), y4)))), Cons(S(S(y5)), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(0), y3), y4)))), Cons(S(0), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(0), y3), y4)))), Cons(S(0), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(Left, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(Left, y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(y6, I(Left, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Nil), Cons(0, z4), I(y6, I(Left, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(y4), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(y4), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(S(y4)), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(S(y4)), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(0), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(0), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Right, y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Right, y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Left, y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Left, y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Write(y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Write(y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(0, y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(0, y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(0, y2), y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(0, y2), y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(0), y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(0), y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Right, I(IfGoto(S(S(y3)), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Right, I(IfGoto(S(S(y3)), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(S(y3), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(S(y3), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(S(y3))), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(S(y3))), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(0)), y3))))), Cons(y4, y5), Cons(0, z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(0)), y3))))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(y3)), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(y3)), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, y9))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y2)), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y2)), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Right, I(IfGoto(S(0), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Right, I(IfGoto(S(0), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(Goto(0), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(Goto(0), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(y4), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(y4), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(0), y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(0), y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(y5, I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), I(y5, I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(Goto(0), y3)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, y4), Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, y4), Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(S(y4)), y5), Cons(0, z4), I(Goto(0), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(0), y4), Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(S(0), y4), Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(0)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), Nil, Cons(0, Cons(y3, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), Nil, Cons(0, Cons(y3, y4)), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), Nil, Cons(0, Cons(0, y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y2))), Nil, Cons(0, 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Cons(0, z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), I(y4, y5)))), z3, Cons(0, z4), I(Goto(S(y8)), I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), I(y4, y5)))), z3, Cons(0, z4), I(Goto(S(y8)), I(y9, y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), I(Goto(0), y4)))), z3, Cons(0, z4), I(Goto(S(y7)), I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), I(Goto(0), y4)))), z3, Cons(0, z4), I(Goto(S(y7)), I(Goto(0), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(y5)), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), I(y3, y4)))), Nil, Cons(0, z4), I(Goto(S(y6)), I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), I(y3, y4)))), Nil, Cons(0, z4), I(Goto(S(y6)), I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), I(Left, I(Goto(0), y3))))), Nil, Cons(0, z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), I(Left, I(Goto(0), y3))))), Nil, Cons(0, z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(y5)), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(y8)), y9)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(y8)), y9))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_1, c6_2, c7_2, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (173) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING[ITE](False, I(IfGoto(0, x0), x1), x2, Cons(S(x3), x4), x5) -> c5(TURING(x1, x2, Cons(S(x3), x4), x5)) by TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(0, y0), y1)), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(S(y4)), z4), z5) -> c5(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y0))), y1)), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), y0), y1)), z2, Cons(S(S(y3)), z4), z5) -> c5(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(S(y1)), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(0), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Left, y0))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Write(y0), y1))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(S(z3), Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(S(z3), Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(S(z3), Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(S(z3), Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(0), y0))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(S(z3), Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(S(z3), Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(S(z3), Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(S(z3), Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(S(y2)), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(S(y2)), z4), I(Goto(0), y4)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(0), z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(Left, y4))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(Left, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(S(S(y5)), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(S(S(y4)), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(Goto(0), y4)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(Goto(0), y5))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(y1)), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(z3), z4), I(Goto(0), y4)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(z3), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y3, I(Goto(S(0)), y4))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y3, I(Goto(S(0)), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(Goto(S(0)), y3)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5))) -> c5(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y3))) -> c5(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(Goto(S(y4)), y5)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c5(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(y0, y1))), Nil, Cons(S(z3), z4), I(Left, I(y3, y4))) -> c5(TURING(I(Left, I(y0, y1)), Nil, Cons(S(z3), z4), I(Left, I(y3, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(S(y1)), z4), I(Left, y3)) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(0), z4), I(Left, y2)) -> c5(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, 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I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(0), y0), y1))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, y5))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y0))), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Right, y1)))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Left, y1)))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(y0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Write(y1), y2)))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z2, Cons(S(z3), Cons(0, y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Goto(0), y1)))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(y0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z2, Cons(S(z3), Cons(S(y6), y7)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Goto(S(S(y1))), y2)))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Goto(S(0)), y1)))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Goto(S(y1)), y2)))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z2, Cons(S(z3), Cons(S(0), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Right, y1)))), z2, Cons(S(z3), Nil), z5) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Right, I(Right, y0)))), z2, Cons(S(z3), Nil), z5) -> c5(TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Right, y1)))), z2, Cons(S(z3), Nil), I(Right, y4)) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Right, y1)))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Right, I(Right, y1)))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y0))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Write(S(y0)), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, 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Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y0))), Nil, Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(y2, y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(y2, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(0, y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(0, y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y0, y1)))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y0)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y0))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y0, y1)))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(Left, y1)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y0)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(IfGoto(S(0), 0), y0), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y0))), y1)), z2, Cons(S(0), z4), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(S(0), S(S(y0))), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y0)), z2, Cons(S(0), z4), I(y3, y4)) -> c5(TURING(I(IfGoto(S(0), S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c5(TURING(I(IfGoto(S(0), S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> 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I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), z3, Cons(0, z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z3, Cons(0, z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(y1, y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(0, y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y1), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y1)), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Cons(y1, y2), Cons(0, z4), z5) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(0, z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y0))), Cons(y1, 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I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y0), y1))), z3, Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y0))), Nil, Cons(0, z4), z5) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, y1))), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(0, z4), 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TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1))))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), I(Goto(0), y6)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), I(Goto(0), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, y3), Cons(0, z4), I(y6, I(Goto(0), y7))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, y3), Cons(0, z4), I(y6, I(Goto(0), y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(0, y2), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(0, y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(S(y2), y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(S(y2), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(S(S(y2)), y3), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(S(S(y2)), y3), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(S(0), y2), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(S(0), y2), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(0, 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I(Goto(0), y5))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(S(y0)), I(Left, I(Goto(0), y1))), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(Goto(0), y1))), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(Goto(0), y0)))), Cons(0, Nil), Cons(0, z4), z5) -> c5(TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(0, y2), Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(0, y2), Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(S(S(y2)), y3), Cons(0, z4), I(Goto(0), y6)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(S(S(y2)), y3), Cons(0, z4), I(Goto(0), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(S(0), y2), Cons(0, z4), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(S(0), y2), Cons(0, z4), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Cons(y2, Cons(y3, y4)), Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, I(Goto(S(0)), y6))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(0)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(y2, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(0, y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y3))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(0)), y4)))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(0)), y4))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), I(y1, y2)))), z3, Cons(0, z4), I(Goto(S(0)), I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(y1, y2))), z3, Cons(0, z4), I(Goto(S(0)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), I(Goto(0), y1)))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(0), y5))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(0)), y1))), z3, Cons(0, 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I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(S(0), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Right, y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Right, y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Left, y3))))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Left, y3))))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Write(y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Write(y3), y4))))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Right, 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I(Left, I(Right, I(IfGoto(S(S(y3)), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(S(y3), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, I(Right, I(IfGoto(S(y3), y4), y5))))), Cons(y6, y7), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(S(y3))), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(S(y3))), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(0)), y3))))), Cons(y4, y5), Cons(0, z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(0)), y3))))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Right, I(Goto(S(y3)), y4))))), Cons(y5, y6), Cons(0, z4), I(y8, 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I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), z4), I(y3, I(Left, I(Goto(S(0)), y4)))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), z4), I(y3, I(Left, I(Goto(S(0)), y4))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(y2), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(y2), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), I(y1, y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(y1, y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), I(Goto(0), y1)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y5))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(y2, y3)), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(y2, y3)), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(0, y2)), I(Goto(S(0)), y3)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(0, y2)), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(y0, y1)))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0))))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(Goto(S(0)), y3)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(y5)), y6)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(y5)), y6))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(S(y1))), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(y2, y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), I(y1, y2)))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y0))), Nil, Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(y2, y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(y2, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(0, y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(0, y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y0, y1)))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(y2), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y0)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y0))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y0, y1)))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5))) -> c5(TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(S(z3), z4), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Left, I(Left, y1)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y0)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(IfGoto(S(0), 0), y0), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y0))), y1)), z2, Cons(S(0), z4), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(S(0), S(S(y0))), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y0)), z2, Cons(S(0), z4), I(y3, y4)) -> c5(TURING(I(IfGoto(S(0), S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c5(TURING(I(IfGoto(S(0), S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, 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Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, 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I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_1, c6_2, c7_2, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING(I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(0, x1), x2), x3, Cons(S(z0), x5), x6)) by TURING(I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), I(Goto(0), y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), I(Goto(0), y4))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(0, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(0, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(0, y1), y2))), Cons(S(y3), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y1), y2))), Cons(S(y3), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(0, y1), y2))), Cons(0, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y1), y2))), Cons(0, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(S(y4)), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(S(y4)), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(S(y4), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y1), y2), y3))), Cons(S(y4), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Left, I(Goto(S(0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Left, I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(0), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y1)), y2), y3))), Cons(S(0), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(0), y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y1), y2))), Cons(S(0), y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Nil), Cons(S(z3), z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(y2), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(y2), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(S(y2)), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(S(y2)), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(0), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(S(0), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Right, I(Right, y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Right, y1)))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Right, I(Left, y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Left, y1)))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Right, I(Write(y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Write(y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(0, y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(0, y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Right, I(Goto(0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5)) 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z2, Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(0), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(0), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(0), y2))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(0), y2))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(y3, y4)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(0, y3)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(0), y2))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Write(y2), y3)))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Write(y2), y3)))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(0, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(0, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(S(y5), y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(S(y5), y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(S(y2))), y3)))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(S(y2))), y3)))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(0)), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(0)), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(0), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(0), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(S(y4)), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(S(y4)), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(0), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(0), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(Left, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(Left, y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(Left, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(Left, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(y3), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(y3), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(S(y3)), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(S(y3)), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(0), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(0), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Right, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Right, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Left, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Left, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Write(y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Write(y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, I(IfGoto(S(y1), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, I(IfGoto(S(y1), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(0, y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(0, y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, I(IfGoto(0, y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, I(IfGoto(0, y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(0), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(0), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(S(y2)), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(S(y2)), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(S(y2))), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(S(y2))), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(0)), y2))))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(0)), y2))))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(0), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(0), y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(y3), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(y3), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), I(Goto(0), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(y1, y2)))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(y1, y2)))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(0)), y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(0)), y4))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, I(Goto(S(y6)), y7)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, I(Goto(S(y6)), y7))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(y3, y4)))), z2, Cons(S(z3), z4), I(Goto(S(y8)), I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(y3, y4)))), z2, Cons(S(z3), z4), I(Goto(S(y8)), I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(Goto(0), y3)))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(Goto(0), y3)))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(Goto(0), y8)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(Goto(S(y5)), y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), I(y2, y3)))), Nil, Cons(S(z3), z4), I(Goto(S(y6)), I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), I(y2, y3)))), Nil, Cons(S(z3), z4), I(Goto(S(y6)), I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), I(Left, I(Goto(0), y2))))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), I(Left, I(Goto(0), y2))))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(y5)), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(y8)), y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(y8)), y9))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(Goto(S(y9)), y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(Goto(S(y9)), y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(S(y0), y1), y2), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> 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-> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, I(Goto(S(0)), y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(y2, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(0, y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y3))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(0)), y4)))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(0)), y4))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(0)), y0))), z3, Cons(0, z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), z3, Cons(0, z4), I(Goto(S(0)), y5)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), z3, Cons(0, z4), I(Goto(S(0)), y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), I(y1, y2)))), z3, Cons(0, z4), I(Goto(S(0)), I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(y1, y2))), z3, Cons(0, z4), I(Goto(S(0)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), I(Goto(0), y1)))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(0), y5))) -> c5(TURING(I(Write(y0), I(Goto(S(0)), I(Goto(0), y1))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(0)), y1))), z3, Cons(0, 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I(Goto(S(0)), I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), y3)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(0, z4), I(Goto(S(0)), y6)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(0, z4), I(Goto(S(0)), y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(0)), y0))), z3, Cons(0, 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y0))), z3, Cons(0, z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y0), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z3, Cons(0, z4), I(y6, y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(y3, y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(y3, y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(0, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(0, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(Left, I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(Left, I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(S(y5)), y6)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(S(y5)), y6))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(y3), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(y3), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(S(y3)), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(0, Cons(S(0), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(0, Cons(S(0), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y0)), 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Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(y5)), y6)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(y5)), y6))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(S(y1))), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(S(y1))), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(y2, y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), I(y1, y2)))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5)))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Goto(S(y4)), I(Left, I(Goto(0), y5))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(y4)), y5)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(0, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), 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I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(S(y5), y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(S(y5), y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(S(y2))), y3)))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(S(S(y2))), 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Cons(S(S(y4)), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(0), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(0), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(Left, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(Left, y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(Left, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(z3), z4), I(y6, I(Left, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(y3), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(y3), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(S(y3)), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(S(y3)), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(0), Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(0), Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Right, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Right, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Left, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Left, y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Write(y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Write(y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, I(IfGoto(S(y1), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Right, 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I(Left, I(Right, I(IfGoto(S(S(y2)), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Right, I(IfGoto(S(y2), y3), y4))))), Cons(y5, y6), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(S(y2))), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(S(y2))), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(0)), y2))))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(0)), y2))))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Right, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(Goto(0), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(0), y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(y3), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(y3), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), I(y5, I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), 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I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Cons(y4, y5)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Cons(y4, y5)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Write(y2), y3))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Write(y2), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(0, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(0, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(0, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(0, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(S(y5)), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(S(y5)), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(S(y5), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y2))), Cons(y3, y4), Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y2))), Cons(y3, y4), Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(0, z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5)) 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Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Write(y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(S(y2), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(S(y2), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(0, y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(0, y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(0, y2), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(IfGoto(0, y2), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(S(y3)), y4), y5))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(S(y3)), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y2), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y2), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Left, y3)))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Left, y3)))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Write(y3), y4)))), z3, Cons(0, Cons(y6, y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Write(y3), y4)))), z3, Cons(0, Cons(y6, y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(IfGoto(S(y3), y4), y5)))), z3, Cons(0, 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TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(y3), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5) -> 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I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), I(Goto(0), y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(0), z4), I(Goto(0), y4))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Cons(y2, Cons(y3, y4)), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Write(y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, 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Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(0), y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(0), y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Right, y2)))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(Right, y2)))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Left, y2)))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(Left, y2)))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Write(y2), y3)))), z2, Cons(S(z3), Cons(y6, y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(Write(y2), y3)))), z2, Cons(S(z3), Cons(y6, y7)), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(IfGoto(S(y2), y3), y4)))), z2, Cons(S(z3), Cons(0, y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(IfGoto(S(y2), y3), y4)))), z2, Cons(S(z3), Cons(0, y7)), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), 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y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), 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Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Write(y2), y3)))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(0, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(0, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), 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c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, 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I(Write(y1), I(Goto(S(0)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Goto(S(0)), y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(y1, y2)))), Nil, Cons(S(z3), z4), I(Goto(S(0)), I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), I(y1, y2)))), Nil, Cons(S(z3), 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y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, I(Goto(S(y6)), y7)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), 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I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_2, c7_2, c6_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1 ---------------------------------------- (177) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(S(x4)), x5), x6) -> c5(TURING(x2, x3, Cons(S(S(x4)), x5), x6)) by TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(S(S(y0)), y1), y2), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(S(y0))), y1)), z3, Cons(S(S(z4)), z5), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(S(S(z4)), z5), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(S(0), y0), y1)), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(S(0), y0), y1), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, y0)), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(z4)), z5), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(z4)), z5), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Cons(y3, y4)), z6) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(S(S(z4)), Cons(y3, y4)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Left, y0))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Write(y0), y1))), z3, Cons(S(S(z4)), Cons(y4, y5)), z6) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(S(S(z4)), Cons(y4, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(S(S(z4)), Cons(0, y5)), z6) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(S(S(z4)), Cons(0, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(S(S(z4)), Cons(S(y4), y5)), z6) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(S(S(z4)), Cons(S(y4), y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(S(S(z4)), Cons(0, y4)), z6) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(S(S(z4)), Cons(0, y4)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Goto(0), y0))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(S(S(z4)), z5), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(S(S(z4)), z5), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(S(S(z4)), z5), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(S(S(z4)), z5), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(S(S(z4)), Cons(S(S(y4)), y5)), z6) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(S(S(z4)), Cons(S(S(y4)), y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(S(S(z4)), Cons(S(0), y4)), z6) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(S(S(z4)), Cons(S(0), y4)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Nil), z6) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(S(S(z4)), Nil), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(S(S(z4)), Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(S(S(z4)), Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(S(S(z4)), Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Goto(0), y0), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z3, Cons(S(S(z4)), z5), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z3, Cons(S(S(z4)), z5), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z3, Cons(S(S(z4)), z5), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(0), y0)), Cons(y1, y2), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(S(S(z4)), z5), I(y4, y5)) -> c5(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(S(z4)), z5), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), 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Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), I(y1, y2))), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), I(y1, y2)), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(Goto(S(y4)), I(Goto(0), y5))) -> c5(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(y4)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, y3)) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(z4)), z5), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(y0, y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(y3, y4))) -> c5(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(z4)), z5), I(Left, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Left, y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y3))) -> c5(TURING(I(Left, I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Write(y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Write(y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(IfGoto(S(y0), y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(y0)), I(IfGoto(0, y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(IfGoto(0, y0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(IfGoto(0, y0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(S(y1)), y2), y3)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(IfGoto(S(y1), y2), y3))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(y0)), I(IfGoto(S(y1), y2), y3)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(S(S(y1))), y2))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Goto(S(S(y1))), y2)), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(S(y0))), I(IfGoto(S(0), y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(IfGoto(S(0), y0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(y4, I(Left, y5))) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(y4, I(Left, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(Left, y1))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(Left, y0))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Cons(y4, y5)), z6) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Cons(y4, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Left, y1)))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Right, I(Left, y1))), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Write(y1), y2)))), z3, Cons(S(S(z4)), Cons(y5, y6)), z6) -> c5(TURING(I(Write(y0), I(Right, I(Write(y1), y2))), z3, Cons(S(S(z4)), Cons(y5, y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(S(S(z4)), Cons(0, y6)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(S(S(z4)), Cons(0, y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(S(S(z4)), Cons(0, y5)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), Cons(0, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Goto(0), y1)))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Right, I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(S(y6)), y7)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), Cons(S(S(y6)), y7)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(y6), y7)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(S(S(z4)), Cons(S(y6), y7)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Goto(S(S(y1))), y2)))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(S(y1))), y2))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Goto(S(0)), y1)))), z3, Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(0)), y1))), z3, Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Goto(S(y1)), y2)))), z3, Cons(S(S(z4)), z5), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Right, I(Goto(S(y1)), y2))), z3, Cons(S(S(z4)), z5), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(0), y6)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), Cons(S(0), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6) -> c5(TURING(I(Write(y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), z6) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Right, I(Right, y0)))), z3, Cons(S(S(z4)), Nil), z6) -> c5(TURING(I(Write(0), I(Right, I(Right, y0))), z3, Cons(S(S(z4)), Nil), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(Right, y4)) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(Right, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(y4, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(y4, I(Right, y5))) -> c5(TURING(I(Write(y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(Goto(0), y5)) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(y5, I(y6, y7))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(0), y6))) -> c5(TURING(I(Write(y0), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(0), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(y0)), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(S(y0))), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(Goto(0), y0))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(0)), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), Cons(y2, y3)), z6) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), Cons(y2, y3)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), Cons(0, y2)), z6) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), Cons(0, y2)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), z5), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(y3, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), z5), I(y3, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), Cons(S(y2), y3)), z6) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), Cons(S(y2), y3)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(0), y0))), Nil, Cons(S(S(z4)), Cons(S(S(y2)), y3)), z6) -> c5(TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(S(S(z4)), Cons(S(S(y2)), y3)), z6)) TURING[ITE](False, 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-> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(Goto(S(y1)), y2))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Goto(S(y1)), y2))), Cons(y3, y4), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(Write(y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(Write(y0), I(Left, I(y1, y2))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), z5), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(Write(S(y0)), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(Write(S(S(y0))), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(Left, y0))), Nil, Cons(S(S(z4)), z5), I(Left, y3)) -> c5(TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), Cons(y2, y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), Cons(y2, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), Cons(0, y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), Cons(0, y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, I(y0, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y4, y5))) -> c5(TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), Cons(S(y2), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), Cons(S(y2), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), Cons(S(S(y2)), y3)), I(Left, y4)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), Cons(S(S(y2)), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, y0))), Nil, Cons(S(S(z4)), Cons(S(0), y2)), I(Left, y3)) -> c5(TURING(I(Write(0), I(Left, y0)), Nil, Cons(S(S(z4)), Cons(S(0), y2)), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4))) -> c5(TURING(I(Write(y0), I(Left, I(Goto(0), y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, I(Goto(0), y0)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y3))) -> c5(TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y0))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(Write(S(S(y0))), I(Left, I(y1, y2))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(0)), I(Left, I(y0, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y4, y5))) -> c5(TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Left, I(Left, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y4))) -> c5(TURING(I(Write(y0), I(Left, I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(IfGoto(0, y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(IfGoto(S(S(y1)), y2), y3)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Goto(S(S(y1))), y2))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8))) -> c5(TURING(I(IfGoto(0, y0), I(Goto(S(S(y1))), y2)), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(IfGoto(S(0), y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(y4, I(Left, y5))) -> c5(TURING(I(IfGoto(0, y0), I(Left, y1)), Nil, Cons(S(S(z4)), z5), I(y4, I(Left, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Cons(y4, y5)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Cons(y4, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Left, y1)))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Left, y1))), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Write(y1), y2)))), z3, Cons(S(S(z4)), Cons(y5, y6)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Write(y1), y2))), z3, Cons(S(S(z4)), Cons(y5, y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(S(S(z4)), Cons(0, y6)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(S(S(z4)), Cons(0, y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), Cons(S(y5), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(0, y1), y2)))), z3, Cons(S(S(z4)), Cons(0, y5)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), Cons(0, y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Goto(0), y1)))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(S(y6)), y7)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), Cons(S(S(y6)), y7)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(y1), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(y6), y7)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(y1), y2), y3))), z3, Cons(S(S(z4)), Cons(S(y6), y7)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Goto(S(S(y1))), y2)))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8))) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Goto(S(S(y1))), y2))), z3, Cons(S(S(z4)), z5), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Goto(S(0)), y1)))), z3, Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Goto(S(0)), y1))), z3, Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Goto(S(y1)), y2)))), z3, Cons(S(S(z4)), z5), I(y6, y7)) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Goto(S(y1)), y2))), z3, Cons(S(S(z4)), z5), I(y6, y7))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(S(y1)), y2), y3)))), z3, Cons(S(S(z4)), Cons(S(0), y6)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), Cons(S(0), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), Cons(S(S(y5)), y6)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(IfGoto(S(0), y1), y2)))), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(IfGoto(S(0), y1), y2))), z3, Cons(S(S(z4)), Cons(S(0), y5)), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), z6) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(Right, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(Right, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(y4, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Right, I(Right, y1)))), z3, Cons(S(S(z4)), Nil), I(y4, I(Right, y5))) -> c5(TURING(I(IfGoto(0, y0), I(Right, I(Right, y1))), z3, Cons(S(S(z4)), Nil), I(y4, I(Right, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Goto(0), y1))), z3, 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Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, y9))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3)))))), Cons(y4, y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3)))))), Cons(y4, y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2)))))), Cons(y3, y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), 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I(y7, I(Goto(0), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(0, y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(S(y3), y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(y3), y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(S(S(y3)), y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(S(0), y3), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1))))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1)))), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y5, I(y6, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y5, I(Left, I(Goto(0), y6)))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y5, I(Left, I(Goto(0), y6))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(y1)), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(y1)), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(Goto(0), y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), 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I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Goto(S(y2)), y3)))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Goto(S(y1)), y2)))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Goto(S(y1)), y2))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, I(Goto(S(y9)), y10))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, I(Goto(S(y9)), y10)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3)))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(y1)), I(Goto(S(y2)), y3)))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(y2, y3))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(y1)), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(y1, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(Left, I(Goto(0), y1)))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(y2, y3))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(y1, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y5))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y5)))) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: lookup(S(z0), I(z1, z2)) -> lookup(z0, z2) lookup(0, z0) -> z0 !EQ(S(z0), S(z1)) -> !EQ(z0, z1) !EQ(0, S(z0)) -> False !EQ(S(z0), 0) -> False !EQ(0, 0) -> True Tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING[ITE](False, I(IfGoto(S(S(x0)), x1), x2), x3, Cons(S(0), x4), x5) -> c5(TURING(x2, x3, Cons(S(0), x4), x5)) TURING[ITE](False, I(IfGoto(S(0), x0), x1), x2, Cons(S(S(x3)), x4), x5) -> c5(TURING(x1, x2, Cons(S(S(x3)), x4), x5)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING[ITE](True, I(IfGoto(0, 0), x1), x2, Cons(0, x3), x4) -> c4(TURING(x4, x2, Cons(0, x3), x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(S(S(x0)), 0), x2), x3, Cons(S(S(x4)), x5), x6) -> c4(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING[ITE](True, I(IfGoto(S(0), 0), x1), x2, Cons(S(0), x3), x4) -> c4(TURING(x4, x2, Cons(S(0), x3), x4), LOOKUP(0, x4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING[ITE](True, I(IfGoto(0, S(S(z1))), x1), x2, Cons(0, x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(0, x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(S(z1))), x2), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x3, Cons(S(S(x4)), x5), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(S(0), S(S(z1))), x1), x2, Cons(S(0), x3), I(z5, I(z6, z7))) -> c4(TURING(lookup(z1, z7), x2, Cons(S(0), x3), I(z5, I(z6, z7))), LOOKUP(S(S(z1)), I(z5, I(z6, z7)))) TURING[ITE](True, I(IfGoto(0, S(0)), x1), x2, Cons(0, x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(0, x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(0)), x2), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c4(TURING(z5, x3, Cons(S(S(x4)), x5), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(S(0), S(0)), x1), x2, Cons(S(0), x3), I(z4, z5)) -> c4(TURING(z5, x2, Cons(S(0), x3), I(z4, z5)), LOOKUP(S(0), I(z4, z5))) TURING[ITE](True, I(IfGoto(0, S(z1)), x1), x2, Cons(0, x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(S(x0)), S(z1)), x2), x3, Cons(S(S(x4)), x5), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING[ITE](True, I(IfGoto(S(0), S(z1)), x1), x2, Cons(S(0), x3), I(z5, z6)) -> c4(LOOKUP(S(z1), I(z5, z6))) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) !EQ'(S(S(S(y0))), S(S(S(y1)))) -> c(!EQ'(S(S(y0)), S(S(y1)))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y0), y1), y2)), z3, Cons(0, z4), z5) -> c5(TURING(I(IfGoto(S(y0), y1), y2), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z3, Cons(0, z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y0)), Nil, Cons(0, z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(0, z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y0), y1))), z3, Cons(0, Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z3, Cons(0, Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y0), y1))), z3, Cons(0, Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z3, Cons(0, Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y0))), z3, Cons(0, z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z3, Cons(0, z4), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y0), y1), y2))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y0))), y1))), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y0))), z3, Cons(0, z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z3, Cons(0, z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y0)), y1))), z3, Cons(0, z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z3, Cons(0, z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z3, Cons(0, Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z3, Cons(0, Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y0), y1))), z3, Cons(0, Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z3, Cons(0, Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y0))), z3, Cons(0, Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z3, Cons(0, Nil), I(y3, I(Right, y4)))) 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y2))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(y3, y4))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(y1), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(S(y1)), y2)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Nil, Cons(0, Cons(S(0), y1)), z5) -> c5(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y0)), Cons(y1, y2), Cons(0, z4), z5) -> 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c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(y3), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(y3), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(S(y3)), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(S(y3)), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(0), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(0), Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Right, I(Right, y2)))), Cons(y3, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Right, y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Right, I(Left, y2)))), Cons(y3, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Left, y2)))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Right, I(Write(y2), y3)))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Right, I(Write(y2), y3)))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, 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I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(S(y3)), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y2), 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I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5)) 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I(Goto(S(y2)), I(Left, I(Goto(0), y3))))), Nil, Cons(0, z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), I(Left, I(Goto(0), y3))))), Nil, Cons(0, z4), I(Goto(S(y5)), I(Left, I(Goto(0), y6))))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(y6)), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(y5)), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(y8)), y9)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(y8)), y9))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(y8, I(Goto(S(y9)), y10)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(S(y3)), y4))), z3, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(y4, y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(0, y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(0, y0), y1)), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(S(y4)), z4), z5) -> c5(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y0))), y1)), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(S(y0))), y1), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), y0), y1)), z2, Cons(S(S(y3)), z4), z5) -> c5(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(z3), z4), I(y2, I(Left, y3))) -> c5(TURING(I(Left, y0), Nil, Cons(S(z3), z4), I(y2, I(Left, y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(S(y1)), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, y0)), Nil, Cons(S(0), z4), z5) -> c5(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Cons(y3, y4)), z5) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Cons(y3, y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Left, y0))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Right, I(Left, y0)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Write(y0), y1))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c5(TURING(I(Right, I(Write(y0), y1)), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(S(z3), Cons(S(y4), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(S(z3), Cons(S(y4), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(S(z3), Cons(0, y4)), z5) -> c5(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(S(z3), Cons(0, y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(0), y0))), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Right, I(Goto(0), y0)), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c5(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(S(z3), Cons(S(S(y4)), y5)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(S(z3), Cons(S(S(y4)), y5)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(S(z3), Cons(S(0), y4)), z5) -> c5(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(S(z3), Cons(S(0), y4)), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), z5) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(Right, y3)) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(Right, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(y3, I(y4, y5))) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y0))), z2, Cons(S(z3), Nil), I(y3, I(Right, y4))) -> c5(TURING(I(Right, I(Right, y0)), z2, Cons(S(z3), Nil), I(y3, I(Right, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(y3, I(Goto(0), y4))) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(z3), z4), I(y3, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(S(y2)), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(0), z4), z5) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(S(y2)), z4), I(Goto(0), y4)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), z2, Cons(S(0), z4), I(Goto(0), y3)) -> c5(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(Left, y3)) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(Left, y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(Left, y4))) -> c5(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(S(z3), z4), I(y3, I(Left, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(S(S(y5)), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(S(S(y4)), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(Goto(0), y4)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(Goto(0), y5))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(y3, y4))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(z3), z4), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(y1)), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(0), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(z3), z4), I(Goto(0), y4)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(z3), z4), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(z3), z4), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(z3), z4), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(S(z3), z4), z5)) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y3, I(Goto(S(0)), y4))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(y3, I(Goto(S(0)), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(Goto(S(0)), y3)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5))) -> c5(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y3))) -> c5(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(z3), z4), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(z3), z4), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(0)), y0)), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4))) -> c5(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(Goto(S(y4)), y5)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(S(z3), z4), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(S(z3), z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c5(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(z3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), 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c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, y5)) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(y2, y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(y2, y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(0, y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(0, y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y3))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y3)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), z4), I(y3, I(y4, y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), z4), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), z4), I(y3, I(Left, I(Goto(S(0)), y4)))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), z4), I(y3, I(Left, I(Goto(S(0)), y4))))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(y2), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(y2), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(y4, y5)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(S(y2)), y3)), I(y4, y5))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(y3, y4)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(y3, y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), 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I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), Nil, Cons(S(z3), Cons(S(0), y2)), I(Goto(S(0)), y3)) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(S(z3), Cons(S(0), y2)), I(Goto(S(0)), y3))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(0)), y1))), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c5(TURING(I(Write(y0), I(Goto(S(0)), y1)), Cons(y2, y3), Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(0)), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y0))), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5))) -> c5(TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(S(z3), z4), I(y4, I(Goto(S(0)), y5)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(y0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c5(TURING(I(Write(y0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(S(y0)), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y0))), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c5(TURING(I(Write(S(S(y0))), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, y7))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c5(TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(S(z3), z4), I(y5, y6))) TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6)) -> c5(TURING(I(Write(0), I(Goto(S(y0)), y1)), 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I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(Goto(S(y5)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(Goto(S(y5)), y6))) TURING(I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), I(y2, y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), I(y2, y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), I(Goto(0), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), I(Goto(0), y7)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(y5, I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(y6, I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(S(y4)), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(y7, I(Goto(S(y8)), y9)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(y1)), y2)), Cons(y3, y4), Cons(S(z3), z4), I(Goto(S(0)), I(Goto(S(y7)), y8)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), I(Left, y3)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), I(Left, y3))) TURING(I(IfGoto(0, z0), I(Left, I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Goto(0), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(S(y3)), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(S(y3)), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(0), z4), I(Left, I(y4, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(y1, y2))), Nil, Cons(S(0), z4), I(Left, I(y4, y5)))) TURING(I(IfGoto(0, z0), I(Left, I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, I(Left, y4)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Write(y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Write(y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(IfGoto(0, y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(IfGoto(0, y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(IfGoto(0, y1), y2))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(IfGoto(0, y1), y2))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(S(y2)), y3), y4))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(S(y2)), y3), y4))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(IfGoto(S(y2), y3), y4))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(IfGoto(S(y2), y3), y4))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(0), y2), y3))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(IfGoto(S(0), y2), y3))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Right, y2)))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(Right, y2)))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Left, y2)))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Right, I(Left, y2)))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Right, I(Write(y2), y3)))), z2, Cons(S(z3), 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I(Write(y1), I(Left, I(Right, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y1)), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(Right, I(IfGoto(S(0), y2), y3))))), Cons(y4, y5), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y1), y2))))), Cons(y3, y4), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, y4), Cons(S(z3), z4), z5) -> 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c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(S(y3)), y4), Cons(S(z3), z4), I(Goto(0), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(S(0), y3), Cons(S(z3), z4), I(Goto(0), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Cons(y3, Cons(y4, y5)), Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(0, y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(0)), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), z4), I(y4, I(Left, I(Goto(S(0)), y5))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(y4, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), Cons(y3, y4), Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(y2, y3)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(0)), I(Goto(0), y2)))), z2, Cons(S(z3), z4), I(Goto(S(0)), I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(Goto(S(0)), y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Goto(S(0)), y5))) TURING(I(IfGoto(0, z0), I(Write(0), 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I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(0)), y2))), z2, Cons(S(z3), z4), I(y6, I(Goto(S(0)), y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, I(Goto(S(0)), y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(y1)), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(y7, y8))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(y4, y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(0, y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(Left, I(Goto(S(y5)), y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, I(Goto(S(y6)), y7)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), z4), I(y5, I(Left, I(Goto(S(y6)), y7))))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(y4), y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(S(y4)), y5)), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(z3), Cons(S(0), y4)), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(Goto(S(y6)), y7))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(z3), z4), I(y8, y9))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), y3))), z2, Cons(S(z3), z4), I(Goto(S(y7)), y8))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(y3, y4)))), z2, Cons(S(z3), z4), I(Goto(S(y8)), I(y9, y10))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(y3, y4)))), z2, Cons(S(z3), z4), I(Goto(S(y8)), I(y9, y10)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(Goto(0), y3)))), z2, Cons(S(z3), z4), I(Goto(S(y7)), I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Goto(S(y2)), I(Goto(0), y3)))), z2, Cons(S(z3), z4), 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Cons(0, y1), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y2, I(y3, y4))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(z4)), z5), I(y2, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(S(S(z4)), z5), I(y2, I(Left, I(Goto(0), y3)))) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(z4)), z5), I(y2, I(Left, I(Goto(0), y3))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(S(S(z4)), z5), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(S(S(z4)), z5), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(S(S(z4)), z5), I(Goto(0), y4)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(S(S(z4)), z5), I(Goto(0), y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(S(S(z4)), z5), I(Goto(0), y3)) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(S(S(z4)), z5), I(Goto(0), y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), z3, Cons(S(S(z4)), z5), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), z3, Cons(S(S(z4)), z5), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), z3, Cons(S(S(z4)), z5), I(y3, I(y4, y5))) -> c5(TURING(I(Goto(S(0)), y0), z3, Cons(S(S(z4)), z5), I(y3, I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), z3, Cons(S(S(z4)), z5), I(y3, I(Goto(S(0)), y4))) -> c5(TURING(I(Goto(S(0)), y0), z3, Cons(S(S(z4)), z5), I(y3, I(Goto(S(0)), y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(S(z4)), z5), I(y4, y5)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(S(z4)), z5), I(y4, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), I(y0, y1))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(y4, y5))) -> c5(TURING(I(Goto(S(0)), I(y0, y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(y4, y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), I(Goto(0), y0))), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(0), y3))) -> c5(TURING(I(Goto(S(0)), I(Goto(0), y0)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(0), y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(S(S(z4)), z5), I(Goto(S(0)), y4)) -> c5(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(S(S(z4)), z5), I(Goto(S(0)), y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(y4, I(y5, y6))) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(y4, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(y6, y7))) -> c5(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), I(y1, y2))), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), I(y6, y7))) -> c5(TURING(I(Goto(S(y0)), I(y1, y2)), z3, Cons(S(S(z4)), z5), I(Goto(S(y5)), I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(Goto(S(y4)), I(Goto(0), y5))) -> c5(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(y4)), I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(y5)), y6)) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(y5)), y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), z3, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(y5, I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, y3)) -> c5(TURING(I(Left, y0), Nil, Cons(S(S(z4)), z5), I(Left, y3))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(y0, y1))), Nil, Cons(S(S(z4)), z5), I(Left, I(y3, y4))) -> c5(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(z4)), z5), I(Left, I(y3, y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Goto(0), y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2))) -> c5(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y2)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Left, I(Left, y0))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y3))) -> c5(TURING(I(Left, I(Left, y0)), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y3)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(y0), I(Write(y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(y0), I(Write(y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(IfGoto(S(y0), y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(y0)), I(IfGoto(0, y1), y2))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(S(y0)), I(IfGoto(0, y1), y2)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(0), I(IfGoto(0, y0), y1))), z3, Cons(S(S(z4)), z5), z6) -> c5(TURING(I(Write(0), I(IfGoto(0, y0), y1)), z3, Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(Write(S(S(y0))), I(IfGoto(S(S(y1)), y2), y3))), z3, Cons(S(S(z4)), z5), z6) -> 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c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Goto(0), y2)))), z3, Cons(S(S(z4)), z5), I(Goto(0), y6)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Goto(0), y2))), z3, Cons(S(S(z4)), z5), I(Goto(0), y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Goto(0), y1)))), z3, Cons(S(S(z4)), z5), I(Goto(0), y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Goto(0), y1))), z3, Cons(S(S(z4)), z5), I(Goto(0), y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Goto(0), y2)))), Cons(y3, y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Goto(0), y2))), Cons(y3, y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(y3, Cons(y4, y5)), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Cons(y4, y5)), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Write(y2), y3))))), Cons(y4, y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Write(y2), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4))))), Cons(0, y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(0, y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3))))), Cons(S(y4), y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(S(y4), y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3))))), Cons(0, y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(0, y2), y3)))), Cons(0, y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4))))), Cons(S(S(y5)), y6), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(S(y5)), y6), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4))))), Cons(S(y5), y6), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(y2), y3), y4)))), Cons(S(y5), y6), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(S(y2))), y3))))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, I(y9, y10))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(S(y2))), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, I(y9, y10)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(0)), y2))))), Cons(y3, y4), Cons(S(S(z4)), z5), I(y7, y8)) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(0)), y2)))), Cons(y3, y4), Cons(S(S(z4)), z5), I(y7, y8))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(y2)), y3))))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, y9)) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), I(y8, y9))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4))))), Cons(S(0), y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(S(y2)), y3), y4)))), Cons(S(0), y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3))))), Cons(S(S(y4)), y5), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(S(y4)), y5), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3))))), Cons(S(0), y4), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(IfGoto(S(0), y2), y3)))), Cons(S(0), y4), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(y3, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(0, Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(0, Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(Left, y6)) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(Left, y6))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(y6, I(y7, y8))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(y6, I(y7, y8)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(y6, I(Left, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(y3, Nil), Cons(S(S(z4)), z5), I(y6, I(Left, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Cons(S(y3), Nil), Cons(S(S(z4)), z5), z6) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Cons(S(y3), Nil), Cons(S(S(z4)), z5), z6)) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, 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I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2)))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Goto(S(y1)), y2))), Nil, Cons(S(S(z4)), Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3)))), Cons(y4, y5), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(S(S(z4)), z5), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(y2, y3))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(y2, y3)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(y1)), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(y1)), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, y2))), Nil, Cons(S(S(z4)), z5), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, y1)))), Nil, Cons(S(S(z4)), z5), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, y1))), Nil, Cons(S(S(z4)), z5), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(y3, y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(0, y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(y1, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(y3), y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Left, y5)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(S(y3)), y4)), I(Left, y5))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, y1)))), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Left, y4)) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, y1))), Nil, Cons(S(S(z4)), Cons(S(0), y3)), I(Left, y4))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y5)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Goto(0), y4)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(0), I(Left, I(Left, I(Goto(0), y1)))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y4)))) -> c5(TURING(I(IfGoto(0, y0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, I(Goto(0), y4))))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(y2, y3))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y6, y7)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(y1, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6))) -> c5(TURING(I(IfGoto(0, y0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(y5, y6)))) TURING[ITE](False, I(IfGoto(S(S(z0)), z1), I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2))))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y5))) -> c5(TURING(I(IfGoto(0, y0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(S(z4)), z5), I(Left, I(Left, y5)))) S tuples: LOOKUP(0, z0) -> c16 TURING(I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](!EQ(z0, z1), I(IfGoto(S(S(z1)), x1), x2), x3, Cons(S(S(z0)), x5), x6), !EQ'(S(S(z0)), S(S(z1)))) TURING(I(Goto(S(S(z0))), x1), x2, x3, I(x4, I(z1, z2))) -> c7(TURING(lookup(z0, z2), x2, x3, I(x4, I(z1, z2))), LOOKUP(S(S(z0)), I(x4, I(z1, z2)))) TURING(I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(S(z0)), x1), x2), x3, Cons(S(0), x5), x6)) TURING(I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6) -> c6(TURING[ITE](False, I(IfGoto(S(0), x1), x2), x3, Cons(S(S(z0)), x5), x6)) TURING(I(Right, z0), Cons(x2, x1), Nil, x4) -> c9(TURING(z0, Cons(0, Cons(x2, x1)), Nil, x4)) TURING(I(Right, z0), Cons(0, x1), Nil, x2) -> c9(TURING(z0, Cons(0, Cons(0, x1)), Nil, x2)) TURING(I(Right, z0), x3, Nil, I(x5, I(x6, x7))) -> c9(TURING(z0, Cons(0, x3), Nil, I(x5, I(x6, x7)))) TURING(I(Right, z0), x2, Nil, I(x4, I(Right, z0))) -> c9(TURING(z0, Cons(0, x2), Nil, I(x4, I(Right, z0)))) TURING(I(Left, z0), Nil, Cons(x1, x3), x4) -> c11(TURING(z0, Nil, Cons(0, Cons(x1, x3)), x4)) TURING(I(Left, z0), Nil, Cons(0, x1), x2) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x1)), x2)) TURING(I(Left, z0), Nil, x4, I(x5, I(x6, x7))) -> c11(TURING(z0, Nil, Cons(0, x4), I(x5, I(x6, x7)))) TURING(I(Left, z0), Nil, x3, I(x4, I(Left, z0))) -> c11(TURING(z0, Nil, Cons(0, x3), I(x4, I(Left, z0)))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), x5)) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), x6) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), x6)) TURING(I(Left, z0), Nil, Cons(S(0), x4), x5) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), x5)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Cons(y2, y3)), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Cons(y2, y3), z4)) TURING(I(Right, I(Left, y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Left, y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(Write(y0), y1)), z1, Cons(z2, Cons(y3, y4)), z4) -> c8(TURING(I(Write(y0), y1), Cons(z2, z1), Cons(y3, y4), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(0, y4)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(0, y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(S(y3), y4)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(S(y3), y4), z4)) TURING(I(Right, I(IfGoto(0, y0), y1)), z1, Cons(z2, Cons(0, y3)), z4) -> c8(TURING(I(IfGoto(0, y0), y1), Cons(z2, z1), Cons(0, y3), z4)) TURING(I(Right, I(Goto(0), y0)), z1, Cons(z2, z3), z4) -> c8(TURING(I(Goto(0), y0), Cons(z2, z1), z3, z4)) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(S(y4)), y5)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(S(y4)), y5), z4)) TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z1, Cons(z2, Cons(S(y4), y5)), z4) -> c8(TURING(I(IfGoto(S(y0), y1), y2), Cons(z2, z1), Cons(S(y4), y5), z4)) TURING(I(Right, I(Goto(S(S(y0))), y1)), z1, Cons(z2, z3), I(y4, I(y5, y6))) -> c8(TURING(I(Goto(S(S(y0))), y1), Cons(z2, z1), z3, I(y4, I(y5, y6)))) TURING(I(Right, I(Goto(S(0)), y0)), z1, Cons(z2, z3), I(y3, y4)) -> c8(TURING(I(Goto(S(0)), y0), Cons(z2, z1), z3, I(y3, y4))) TURING(I(Right, I(Goto(S(y0)), y1)), z1, Cons(z2, z3), I(y4, y5)) -> c8(TURING(I(Goto(S(y0)), y1), Cons(z2, z1), z3, I(y4, y5))) TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z1, Cons(z2, Cons(S(0), y4)), z4) -> c8(TURING(I(IfGoto(S(S(y0)), y1), y2), Cons(z2, z1), Cons(S(0), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(S(y3)), y4)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(S(y3)), y4), z4)) TURING(I(Right, I(IfGoto(S(0), y0), y1)), z1, Cons(z2, Cons(S(0), y3)), z4) -> c8(TURING(I(IfGoto(S(0), y0), y1), Cons(z2, z1), Cons(S(0), y3), z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), z4) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(0, Nil), z4) -> c8(TURING(I(Right, y0), Cons(0, z1), Nil, z4)) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(Right, y2)) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(Right, y2))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(y3, y4))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(y3, y4)))) TURING(I(Right, I(Right, y0)), z1, Cons(z2, Nil), I(y2, I(Right, y3))) -> c8(TURING(I(Right, y0), Cons(z2, z1), Nil, I(y2, I(Right, y3)))) TURING(I(Goto(0), z0), x2, Cons(x1, x3), x4) -> c7(TURING(x4, x2, Cons(x1, x3), x4), LOOKUP(0, x4)) TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, x2, I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x3, x4, I(x5, I(x6, x7))) -> c7(TURING(I(x5, I(x6, x7)), x3, x4, I(x5, I(x6, x7))), LOOKUP(0, I(x5, I(x6, x7)))) TURING(I(Goto(0), z0), x2, x3, I(x4, I(Goto(0), z0))) -> c7(TURING(I(x4, I(Goto(0), z0)), x2, x3, I(x4, I(Goto(0), z0))), LOOKUP(0, I(x4, I(Goto(0), z0)))) TURING(I(Goto(0), z0), x3, Cons(0, x4), x5) -> c7(TURING(x5, x3, Cons(0, x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x2, Cons(S(x3), x4), x5) -> c7(TURING(x5, x2, Cons(S(x3), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), x3, Cons(S(S(x4)), x5), x6) -> c7(TURING(x6, x3, Cons(S(S(x4)), x5), x6), LOOKUP(0, x6)) TURING(I(Goto(0), z0), x3, Cons(S(0), x4), x5) -> c7(TURING(x5, x3, Cons(S(0), x4), x5), LOOKUP(0, x5)) TURING(I(Goto(0), z0), Cons(0, Cons(x1, x2)), Nil, x3) -> c7(TURING(x3, Cons(0, Cons(x1, x2)), Nil, x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Cons(0, Cons(0, x1)), Nil, x2) -> c7(TURING(x2, Cons(0, Cons(0, x1)), Nil, x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))) -> c7(TURING(I(Right, I(Goto(0), z0)), Cons(0, x1), Nil, I(Right, I(Goto(0), z0))), LOOKUP(0, I(Right, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Right, I(Goto(0), z0))), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Right, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(x1, x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(x1, x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(0, x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(0, x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))) -> c7(TURING(I(Left, I(Goto(0), z0)), Nil, Cons(0, x1), I(Left, I(Goto(0), z0))), LOOKUP(0, I(Left, I(Goto(0), z0)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x2, I(x3, x4)), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(0, I(x2, I(x3, x4)))) TURING(I(Goto(0), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))) -> c7(TURING(I(x2, I(Left, I(Goto(0), z0))), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(0), z0)))), LOOKUP(0, I(x2, I(Left, I(Goto(0), z0))))) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(x1), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(x1), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), x3) -> c7(TURING(x3, Nil, Cons(0, Cons(S(S(x1)), x2)), x3), LOOKUP(0, x3)) TURING(I(Goto(0), z0), Nil, Cons(0, Cons(S(0), x1)), x2) -> c7(TURING(x2, Nil, Cons(0, Cons(S(0), x1)), x2), LOOKUP(0, x2)) TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(0, x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x2, Cons(S(S(x3)), x4), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)) -> c7(TURING(I(Goto(0), z0), x1, Cons(S(0), x2), I(Goto(0), z0)), LOOKUP(0, I(Goto(0), z0))) TURING(I(Goto(0), x0), Cons(x2, x1), x3, x4) -> c7(TURING(x4, Cons(x2, x1), x3, x4), LOOKUP(0, x4)) TURING(I(Left, I(Left, y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Left, y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Left, I(Write(y0), y1)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Write(y0), y1), z2, Cons(z1, z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y3), z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z3), z4)) TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, z2), z3, z4) -> c10(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z3), z4)) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y4)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z3), z4)) TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y4), z2), z3, z4) -> c10(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z3), z4)) TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(z1, z2), z3, I(y4, I(y5, y6))) -> c10(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z1, z3), I(y4, I(y5, y6)))) TURING(I(Left, I(Goto(S(0)), y0)), Cons(z1, z2), z3, I(y3, y4)) -> c10(TURING(I(Goto(S(0)), y0), z2, Cons(z1, z3), I(y3, y4))) TURING(I(Left, I(Goto(S(y0)), y1)), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Goto(S(y0)), y1), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y3)), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z3), z4)) TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(0, Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(0, z3), z4)) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(Left, y2)) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(Left, y2))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Left, y0)), Cons(z1, Nil), z3, I(y2, I(Left, y3))) -> c10(TURING(I(Left, y0), Nil, Cons(z1, z3), I(y2, I(Left, y3)))) TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(y1), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z3), z4)) TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), z3, z4) -> c10(TURING(I(Left, y0), Nil, Cons(S(0), z3), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Cons(y3, y4), z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Cons(y3, y4)), z4)) TURING(I(Left, I(Right, I(Left, y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Left, y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(z1, z2), Cons(y4, y5), z4) -> c10(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z1, Cons(y4, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(0, y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(0, y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(S(y4), y5), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(S(y4), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(z1, z2), Cons(0, y4), z4) -> c10(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z1, Cons(0, y4)), z4)) TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(z1, z2), z3, z4) -> c10(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(S(y5)), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(S(y5)), y6)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(z1, z2), Cons(S(y5), y6), z4) -> c10(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z1, Cons(S(y5), y6)), z4)) TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(z1, z2), z3, I(y5, I(y6, y7))) -> c10(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z1, z3), I(y5, I(y6, y7)))) TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(z1, z2), z3, I(y4, y5)) -> c10(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z1, z3), I(y4, y5))) TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(z1, z2), z3, I(y5, y6)) -> c10(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z1, z3), I(y5, y6))) TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(z1, z2), Cons(S(0), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z1, Cons(S(0), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(S(y4)), y5), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(S(y4)), y5)), z4)) TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(z1, z2), Cons(S(0), y4), z4) -> c10(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z1, Cons(S(0), y4)), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(0, z2), Nil, z4) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z4)) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(Right, y3)) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(Right, y3))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(y4, y5))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(y4, y5)))) TURING(I(Left, I(Right, I(Right, y0))), Cons(z1, z2), Nil, I(y3, I(Right, y4))) -> c10(TURING(I(Right, I(Right, y0)), z2, Cons(z1, Nil), I(y3, I(Right, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(y4, y5))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(y4, y5)))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, z2), z3, I(y3, I(Goto(0), y4))) -> c10(TURING(I(Goto(0), y0), z2, Cons(z1, z3), I(y3, I(Goto(0), y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(y2), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(y2), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, z4) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(y1, y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(Left, I(Goto(0), y2))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(Left, I(Goto(0), y2)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(y3, y4))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(y3, y4)))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), z3, I(y2, I(Left, I(Goto(0), y3)))) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, z3), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), y2), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), y1), z4) -> c10(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z4)) TURING(I(Left, I(Goto(0), y0)), Cons(0, z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(0, z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y2)), z2), z3, I(Goto(0), y4)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z3), I(Goto(0), y4))) TURING(I(Left, I(Goto(0), y0)), Cons(S(0), z2), z3, I(Goto(0), y3)) -> c10(TURING(I(Goto(0), y0), z2, Cons(S(0), z3), I(Goto(0), y3))) TURING(I(Left, I(Goto(0), y0)), Cons(z1, Cons(y1, y2)), z3, z4) -> c10(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z1, z3), z4)) TURING(I(Goto(S(0)), z0), x2, Cons(x0, x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(x0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, x3, I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, x3, I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, x2, I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x3, Cons(0, x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(0, x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x2, Cons(S(x3), x4), I(z3, z4)) -> c7(TURING(z4, x2, Cons(S(x3), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(S(x4)), x5), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x3, Cons(S(0), x4), I(z3, z4)) -> c7(TURING(z4, x3, Cons(S(0), x4), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(x1, x2)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(z3, z4)) -> c7(TURING(z4, Cons(0, Cons(0, x1)), Nil, I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Right, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))) -> c7(TURING(I(Right, I(Goto(S(0)), z0)), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Right, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(x1, x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(0, x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), z0))), LOOKUP(S(0), I(Left, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(x2, I(x3, x4))), LOOKUP(S(0), I(x2, I(x3, x4)))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))) -> c7(TURING(I(Left, I(Goto(S(0)), z0)), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(0)), z0)))), LOOKUP(S(0), I(x2, I(Left, I(Goto(S(0)), z0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(x1), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(S(x1)), x2)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)) -> c7(TURING(z4, Nil, Cons(0, Cons(S(0), x1)), I(z3, z4)), LOOKUP(S(0), I(z3, z4))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(0, x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)) -> c7(TURING(z0, x2, Cons(S(S(x3)), x4), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(0), x2), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(TURING(x5, Cons(x2, x1), x3, I(x4, x5)), LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(0)), z0), x1, Cons(x2, x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(x2, x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x4, x5)), x1, x2, I(Goto(S(0)), I(x4, x5))) -> c7(TURING(I(x4, x5), x1, x2, I(Goto(S(0)), I(x4, x5))), LOOKUP(S(0), I(Goto(S(0)), I(x4, x5)))) TURING(I(Goto(S(0)), I(Goto(0), x0)), x1, x2, I(Goto(S(0)), I(Goto(0), x0))) -> c7(TURING(I(Goto(0), x0), x1, x2, I(Goto(S(0)), I(Goto(0), x0))), LOOKUP(S(0), I(Goto(S(0)), I(Goto(0), x0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(x2), x3), I(Goto(S(0)), z0)) -> c7(TURING(z0, x1, Cons(S(x2), x3), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Cons(0, x1), Nil, I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))) -> c7(TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Goto(S(0)), I(Right, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))) -> c7(TURING(I(x3, x4), Nil, Cons(0, x1), I(Goto(S(0)), I(x3, x4))), LOOKUP(S(0), I(Goto(S(0)), I(x3, x4)))) TURING(I(Goto(S(0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))) -> c7(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Goto(S(0)), I(Left, I(Goto(0), x0)))), LOOKUP(S(0), I(Goto(S(0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)) -> c7(TURING(z0, Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), Cons(x1, x2), x3, I(Goto(S(0)), z0)) -> c7(TURING(z0, Cons(x1, x2), x3, I(Goto(S(0)), z0)), LOOKUP(S(0), I(Goto(S(0)), z0))) TURING(I(Goto(S(0)), z0), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(0, x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(TURING(I(x7, x8), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))), LOOKUP(S(0), I(x6, I(x7, x8)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(TURING(I(x5, x6), x2, Cons(S(0), x3), I(x4, I(x5, x6))), LOOKUP(S(0), I(x4, I(x5, x6)))) TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x5, I(Goto(S(0)), z0)))) TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))) -> c7(TURING(I(Goto(S(0)), z0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), z0))), LOOKUP(S(0), I(x3, I(Goto(S(0)), z0)))) TURING(I(Right, I(x5, x6)), x2, Nil, I(Right, I(x5, x6))) -> c9(TURING(I(x5, x6), Cons(0, x2), Nil, I(Right, I(x5, x6)))) TURING(I(Right, z0), Cons(0, Cons(x1, x2)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(x1, x2))), Nil, I(Right, z0))) TURING(I(Right, z0), Cons(0, Cons(0, x1)), Nil, I(Right, z0)) -> c9(TURING(z0, Cons(0, Cons(0, Cons(0, x1))), Nil, I(Right, z0))) TURING(I(Right, I(x3, x4)), Cons(0, x1), Nil, I(Right, I(x3, x4))) -> c9(TURING(I(x3, x4), Cons(0, Cons(0, x1)), Nil, I(Right, I(x3, x4)))) TURING(I(Right, x0), Cons(x2, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(x2, x1)), Nil, I(Right, x0))) TURING(I(Right, x0), Cons(0, x1), Nil, I(Right, x0)) -> c9(TURING(x0, Cons(0, Cons(0, x1)), Nil, I(Right, x0))) TURING(I(Right, I(x4, x5)), Cons(x2, x1), Nil, I(Right, I(x4, x5))) -> c9(TURING(I(x4, x5), Cons(0, Cons(x2, x1)), Nil, I(Right, I(x4, x5)))) TURING(I(Right, I(Right, x4)), Cons(x2, x1), Nil, I(Right, I(Right, x4))) -> c9(TURING(I(Right, x4), Cons(0, Cons(x2, x1)), Nil, I(Right, I(Right, x4)))) TURING(I(Right, I(Goto(0), x0)), x1, Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, x1), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Goto(0), x0)), Cons(0, x1), Nil, I(Right, I(Goto(0), x0))) -> c9(TURING(I(Goto(0), x0), Cons(0, Cons(0, x1)), Nil, I(Right, I(Goto(0), x0)))) TURING(I(Right, I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Right, I(Right, I(Goto(0), x0)))) -> c9(TURING(I(Right, I(Goto(0), x0)), Cons(0, Cons(0, x1)), Nil, I(Right, I(Right, I(Goto(0), x0))))) TURING(I(Left, z0), Nil, Cons(x0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(x0, x4)), I(Left, z0))) TURING(I(Left, I(x5, x6)), Nil, x3, I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, x3), I(Left, I(x5, x6)))) TURING(I(Left, z0), Nil, Cons(0, x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(x3), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(x3), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(S(x4)), x5), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(S(0), x4), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(S(0), x4)), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(x1, x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(x1, x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(0, x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(0, x1))), I(Left, z0))) TURING(I(Left, I(x3, x4)), Nil, Cons(0, x1), I(Left, I(x3, x4))) -> c11(TURING(I(x3, x4), Nil, Cons(0, Cons(0, x1)), I(Left, I(x3, x4)))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(x1), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(x1), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(S(x1)), x2))), I(Left, z0))) TURING(I(Left, z0), Nil, Cons(0, Cons(S(0), x1)), I(Left, z0)) -> c11(TURING(z0, Nil, Cons(0, Cons(0, Cons(S(0), x1))), I(Left, z0))) TURING(I(Left, I(Goto(0), x0)), Nil, x2, I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, x2), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, x1), I(Left, I(Goto(0), x0))) -> c11(TURING(I(Goto(0), x0), Nil, Cons(0, Cons(0, x1)), I(Left, I(Goto(0), x0)))) TURING(I(Left, I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Left, I(Left, I(Goto(0), x0)))) -> c11(TURING(I(Left, I(Goto(0), x0)), Nil, Cons(0, Cons(0, x1)), I(Left, I(Left, I(Goto(0), x0))))) TURING(I(Left, I(x7, x8)), Nil, Cons(S(S(x4)), x5), I(Left, I(x7, x8))) -> c11(TURING(I(x7, x8), Nil, Cons(0, Cons(S(S(x4)), x5)), I(Left, I(x7, x8)))) TURING(I(Left, I(x5, x6)), Nil, Cons(S(0), x3), I(Left, I(x5, x6))) -> c11(TURING(I(x5, x6), Nil, Cons(0, Cons(S(0), x3)), I(Left, I(x5, x6)))) TURING(I(Left, I(x4, x5)), Nil, Cons(x1, x2), I(Left, I(x4, x5))) -> c11(TURING(I(x4, x5), Nil, Cons(0, Cons(x1, x2)), I(Left, I(x4, x5)))) TURING(I(Left, I(Left, x4)), Nil, Cons(x1, x2), I(Left, I(Left, x4))) -> c11(TURING(I(Left, x4), Nil, Cons(0, Cons(x1, x2)), I(Left, I(Left, x4)))) TURING(I(Write(z0), I(Write(y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Write(y0), y1), z2, Cons(z0, z4), z5)) TURING(I(Write(0), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(0, z4), z5)) TURING(I(Write(S(y3)), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(S(y3), z4), z5)) TURING(I(Write(0), I(IfGoto(0, y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(0, y0), y1), z2, Cons(0, z4), z5)) TURING(I(Write(S(S(y4))), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(y4)), I(IfGoto(S(y0), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(y0), y1), y2), z2, Cons(S(y4), z4), z5)) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(S(y0))), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(S(y0)), y1), y2), z2, Cons(S(0), z4), z5)) TURING(I(Write(S(S(y3))), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(S(y3)), z4), z5)) TURING(I(Write(S(0)), I(IfGoto(S(0), y0), y1)), z2, Cons(z3, z4), z5) -> c12(TURING(I(IfGoto(S(0), y0), y1), z2, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(y2, I(Left, y3))) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(y2, I(Left, y3)))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), z5) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Cons(y3, y4)), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Cons(y3, y4)), z5)) TURING(I(Write(z0), I(Right, I(Left, y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Left, y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(Write(y0), y1))), z2, Cons(z3, Cons(y4, y5)), z5) -> c12(TURING(I(Right, I(Write(y0), y1)), z2, Cons(z0, Cons(y4, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(0, y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(0, y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(S(y4), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(S(y4), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(0, y0), y1))), z2, Cons(z3, Cons(0, y4)), z5) -> c12(TURING(I(Right, I(IfGoto(0, y0), y1)), z2, Cons(z0, Cons(0, y4)), z5)) TURING(I(Write(z0), I(Right, I(Goto(0), y0))), z2, Cons(z3, z4), z5) -> c12(TURING(I(Right, I(Goto(0), y0)), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(S(y5)), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(S(y5)), y6)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(y0), y1), y2))), z2, Cons(z3, Cons(S(y5), y6)), z5) -> c12(TURING(I(Right, I(IfGoto(S(y0), y1), y2)), z2, Cons(z0, Cons(S(y5), y6)), z5)) TURING(I(Write(z0), I(Right, I(Goto(S(S(y0))), y1))), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Right, I(Goto(S(S(y0))), y1)), z2, Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Right, I(Goto(S(0)), y0))), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Right, I(Goto(S(0)), y0)), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Right, I(Goto(S(y0)), y1))), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Right, I(Goto(S(y0)), y1)), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Right, I(IfGoto(S(S(y0)), y1), y2))), z2, Cons(z3, Cons(S(0), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(S(y0)), y1), y2)), z2, Cons(z0, Cons(S(0), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(S(y4)), y5)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(S(y4)), y5)), z5)) TURING(I(Write(z0), I(Right, I(IfGoto(S(0), y0), y1))), z2, Cons(z3, Cons(S(0), y4)), z5) -> c12(TURING(I(Right, I(IfGoto(S(0), y0), y1)), z2, Cons(z0, Cons(S(0), y4)), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), z5)) TURING(I(Write(0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), z5) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(0, Nil), z5)) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(Right, y3)) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(Right, y3))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(y4, y5))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Right, I(Right, y0))), z2, Cons(z3, Nil), I(y3, I(Right, y4))) -> c12(TURING(I(Right, I(Right, y0)), z2, Cons(z0, Nil), I(y3, I(Right, y4)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(0), y0)), z2, Cons(z3, z4), I(y3, I(Goto(0), y4))) -> c12(TURING(I(Goto(0), y0), z2, Cons(z0, z4), I(y3, I(Goto(0), y4)))) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), z5)) TURING(I(Write(S(y2)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(y2), z4), z5)) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), z5)) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(y1, y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(y1, y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(0, y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(0, y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(y1), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(y1), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), z5)) TURING(I(Write(0), I(Goto(0), y0)), Nil, Cons(z3, Cons(S(0), y1)), z5) -> c12(TURING(I(Goto(0), y0), Nil, Cons(0, Cons(S(0), y1)), z5)) TURING(I(Write(0), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(0, z4), I(Goto(0), y3))) TURING(I(Write(S(S(y2))), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(S(y2)), z4), I(Goto(0), y4))) TURING(I(Write(S(0)), I(Goto(0), y0)), z2, Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Goto(0), y0), z2, Cons(S(0), z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Goto(0), y0)), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Goto(0), y0), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Write(y0), y1))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Write(y0), y1)), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(0, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(0, y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(S(y2), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(S(y2), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(0, y0), y1))), Cons(0, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(0, y0), y1)), Cons(0, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(S(y3)), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(S(y3)), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(y0), y1), y2))), Cons(S(y3), y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(y0), y1), y2)), Cons(S(y3), y4), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Left, I(IfGoto(S(S(y0)), y1), y2))), Cons(S(0), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(S(y0)), y1), y2)), Cons(S(0), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(S(y2)), y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(S(y2)), y3), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(IfGoto(S(0), y0), y1))), Cons(S(0), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(IfGoto(S(0), y0), y1)), Cons(S(0), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(y1, Nil), Cons(z3, z4), I(y3, I(Left, y4))) -> c12(TURING(I(Left, I(Left, y0)), Cons(y1, Nil), Cons(z0, z4), I(y3, I(Left, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(y1), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(y1), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(S(y1)), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(S(y1)), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Left, y0))), Cons(S(0), Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Left, y0)), Cons(S(0), Nil), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Right, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Right, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Left, y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Left, y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Write(y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Write(y0), y1))), Cons(y2, y3), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(Write(S(y4)), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(S(y4), z4), z5)) TURING(I(Write(0), I(Left, I(Right, I(IfGoto(0, y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(0, y0), y1))), Cons(y2, y3), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(0), y0)))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(Goto(0), y0))), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(S(S(y5))), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(S(y5)), z4), z5)) TURING(I(Write(S(y5)), I(Left, I(Right, I(IfGoto(S(y0), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(y0), y1), y2))), Cons(y3, y4), Cons(S(y5), z4), z5)) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(S(y0))), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Left, I(Right, I(Goto(S(S(y0))), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(0)), y0)))), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Left, I(Right, I(Goto(S(0)), y0))), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Left, I(Right, I(Goto(S(y0)), y1)))), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Left, I(Right, I(Goto(S(y0)), y1))), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2)))), Cons(y3, y4), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(S(y0)), y1), y2))), Cons(y3, y4), Cons(S(0), z4), z5)) TURING(I(Write(S(S(y4))), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(S(y4)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Right, I(IfGoto(S(0), y0), y1)))), Cons(y2, y3), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Right, I(IfGoto(S(0), y0), y1))), Cons(y2, y3), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, y2), Cons(z3, z4), I(y4, I(Goto(0), y5))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, y2), Cons(z0, z4), I(y4, I(Goto(0), y5)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(y1), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(y1), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), z5)) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), I(y2, I(Left, I(Goto(0), y3)))) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(z0, z4), I(y2, I(Left, I(Goto(0), y3))))) TURING(I(Write(S(y1)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(y1), z4), z5)) TURING(I(Write(S(S(y1))), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(S(y1)), z4), z5)) TURING(I(Write(S(0)), I(Left, I(Goto(0), y0))), Cons(0, Nil), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, Nil), Cons(S(0), z4), z5)) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(0, y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(0, y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(S(y1)), y2), Cons(z3, z4), I(Goto(0), y4)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(S(y1)), y2), Cons(z0, z4), I(Goto(0), y4))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(S(0), y1), Cons(z3, z4), I(Goto(0), y3)) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(S(0), y1), Cons(z0, z4), I(Goto(0), y3))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Cons(y1, Cons(y2, y3)), Cons(z3, z4), z5) -> c12(TURING(I(Left, I(Goto(0), y0)), Cons(y1, Cons(y2, y3)), Cons(z0, z4), z5)) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, y4))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(y4, y5))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, y5))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(Left, I(Goto(S(0)), y2))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(Left, I(Goto(S(0)), y2)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(y3, y4))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, z4), I(y2, I(Left, I(Goto(S(0)), y3)))) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, z4), I(y2, I(Left, I(Goto(S(0)), y3))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(y2, y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(y2, y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(Goto(S(0)), y3))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(Goto(S(0)), y4))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(Goto(S(0)), y3))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(y4, y5))) TURING(I(Write(z0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(z0), I(Goto(S(0)), I(y0, y1))), z2, Cons(z3, z4), I(Goto(S(0)), I(y4, y5))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), z2, Cons(z0, z4), I(Goto(S(0)), I(y4, y5)))) TURING(I(Write(z0), I(Goto(S(0)), I(Goto(0), y0))), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(0), y3))) -> c12(TURING(I(Goto(S(0)), I(Goto(0), y0)), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(0), y3)))) TURING(I(Write(S(y2)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(y2), z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(y1, y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(y1, y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(0, y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(0, y1)), I(Goto(S(0)), y2))) TURING(I(Write(0), I(Goto(S(0)), I(y0, y1))), Nil, Cons(z3, z4), I(Goto(S(0)), I(y3, y4))) -> c12(TURING(I(Goto(S(0)), I(y0, y1)), Nil, Cons(0, z4), I(Goto(S(0)), I(y3, y4)))) TURING(I(Write(0), I(Goto(S(0)), I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Goto(S(0)), I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Goto(S(0)), I(Left, I(Goto(0), y2))))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(y1), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Goto(S(0)), y3))) TURING(I(Write(0), I(Goto(S(0)), y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Goto(S(0)), y2)) -> c12(TURING(I(Goto(S(0)), y0), Nil, Cons(0, Cons(S(0), y1)), I(Goto(S(0)), y2))) TURING(I(Write(z0), I(Goto(S(0)), y0)), Cons(y1, y2), Cons(z3, z4), I(Goto(S(0)), y4)) -> c12(TURING(I(Goto(S(0)), y0), Cons(y1, y2), Cons(z0, z4), I(Goto(S(0)), y4))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(y5, y6)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(0, z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(S(S(y2))), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y4, I(Goto(S(0)), y5))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(S(y2)), z4), I(y4, I(Goto(S(0)), y5)))) TURING(I(Write(S(0)), I(Goto(S(0)), y0)), z2, Cons(z3, z4), I(y3, I(Goto(S(0)), y4))) -> c12(TURING(I(Goto(S(0)), y0), z2, Cons(S(0), z4), I(y3, I(Goto(S(0)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, y5))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, y6))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Left, I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Left, I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(y4, y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(y4, y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Left, I(Goto(S(y4)), y5)))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Left, I(Goto(S(y4)), y5))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, y4))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(y4)), y5))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(y5)), y6))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(y4)), y5))) TURING(I(Write(z0), I(Goto(S(S(y0))), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(S(y0))), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, y6))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(z0), I(Goto(S(y0)), I(y1, y2))), z2, Cons(z3, z4), I(Goto(S(y5)), I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), z2, Cons(z0, z4), I(Goto(S(y5)), I(y6, y7)))) TURING(I(Write(z0), I(Goto(S(y0)), I(Goto(0), y1))), z2, Cons(z3, z4), I(Goto(S(y4)), I(Goto(0), y5))) -> c12(TURING(I(Goto(S(y0)), I(Goto(0), y1)), z2, Cons(z0, z4), I(Goto(S(y4)), I(Goto(0), y5)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(y3)), y4))) TURING(I(Write(0), I(Goto(S(y0)), I(y1, y2))), Nil, Cons(z3, z4), I(Goto(S(y4)), I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), I(y1, y2)), Nil, Cons(0, z4), I(Goto(S(y4)), I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), I(Left, I(Goto(0), y1)))), Nil, Cons(z3, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4)))) -> c12(TURING(I(Goto(S(y0)), I(Left, I(Goto(0), y1))), Nil, Cons(0, z4), I(Goto(S(y3)), I(Left, I(Goto(0), y4))))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(y4)), y5))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(y3)), y4)) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(y3)), y4))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(y5)), y6)) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(y5)), y6))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(y6, y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(y6, y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(y5, y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(y5, y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(y4, I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(y3, I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(S(S(y3))), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(S(y3)), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(0)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(0), z4), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(y5, I(Goto(S(y6)), y7))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(y5, I(Goto(S(y6)), y7)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(S(y3)), I(Goto(S(y0)), y1)), z2, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), z2, Cons(S(y3), z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(y2, y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(0, y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, z4), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(y2), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(S(y2)), y3)), I(Goto(S(0)), I(Goto(S(y4)), y5)))) TURING(I(Write(0), I(Goto(S(y0)), y1)), Nil, Cons(z3, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4))) -> c12(TURING(I(Goto(S(y0)), y1), Nil, Cons(0, Cons(S(0), y2)), I(Goto(S(0)), I(Goto(S(y3)), y4)))) TURING(I(Write(z0), I(Goto(S(y0)), y1)), Cons(y2, y3), Cons(z3, z4), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c12(TURING(I(Goto(S(y0)), y1), Cons(y2, y3), Cons(z0, z4), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(Write(z0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(z0, z4), I(Left, y3))) TURING(I(Write(z0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(z0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, z4), I(Left, y2))) TURING(I(Write(S(y1)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(y1), z4), I(Left, y3))) TURING(I(Write(S(S(y1))), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(S(S(y1)), z4), I(Left, y3))) TURING(I(Write(S(0)), I(Left, y0)), Nil, Cons(z3, z4), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(S(0), z4), I(Left, y2))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(y1, y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(y1, y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(0, y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(0, y1)), I(Left, y2))) TURING(I(Write(0), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(0, z4), I(Left, I(y3, y4)))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(y1), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(y1), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(S(y1)), y2)), I(Left, y3)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(S(y1)), y2)), I(Left, y3))) TURING(I(Write(0), I(Left, y0)), Nil, Cons(z3, Cons(S(0), y1)), I(Left, y2)) -> c12(TURING(I(Left, y0), Nil, Cons(0, Cons(S(0), y1)), I(Left, y2))) TURING(I(Write(z0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(z0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Goto(0), y0))), Nil, Cons(z3, z4), I(Left, I(Goto(0), y2))) -> c12(TURING(I(Left, I(Goto(0), y0)), Nil, Cons(0, z4), I(Left, I(Goto(0), y2)))) TURING(I(Write(0), I(Left, I(Left, I(Goto(0), y0)))), Nil, Cons(z3, z4), I(Left, I(Left, I(Goto(0), y2)))) -> c12(TURING(I(Left, I(Left, I(Goto(0), y0))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y2))))) TURING(I(Write(S(S(y2))), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y4, y5))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(S(y2)), z4), I(Left, I(y4, y5)))) TURING(I(Write(S(0)), I(Left, I(y0, y1))), Nil, Cons(z3, z4), I(Left, I(y3, y4))) -> c12(TURING(I(Left, I(y0, y1)), Nil, Cons(S(0), z4), I(Left, I(y3, y4)))) TURING(I(Write(z0), I(Left, I(Left, y0))), Nil, Cons(z3, z4), I(Left, I(Left, y3))) -> c12(TURING(I(Left, I(Left, y0)), Nil, Cons(z0, z4), I(Left, I(Left, y3)))) LOOKUP(S(S(y0)), I(z1, I(y1, y2))) -> c15(LOOKUP(S(y0), I(y1, y2))) LOOKUP(S(0), I(z1, z2)) -> c15(LOOKUP(0, z2)) TURING(I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4) -> c6(TURING[ITE](True, I(IfGoto(0, 0), z1), z2, Cons(0, z3), z4)) TURING(I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(0, S(S(y0))), z1), z2, Cons(0, z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(0, S(0)), z1), z2, Cons(0, z3), I(y3, y4))) TURING(I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(0, S(y0)), z1), z2, Cons(0, z3), I(y4, y5))) TURING(I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4) -> c6(TURING[ITE](True, I(IfGoto(S(0), 0), z1), z2, Cons(S(0), z3), z4)) TURING(I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6))) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(S(y0))), z1), z2, Cons(S(0), z3), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(0)), z1), z2, Cons(S(0), z3), I(y3, y4))) TURING(I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5)) -> c6(TURING[ITE](True, I(IfGoto(S(0), S(y0)), z1), z2, Cons(S(0), z3), I(y4, y5))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(S(y2), y3), y4)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, y2)), Nil, Cons(0, z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Cons(y4, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Left, y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Write(y2), y3))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(0, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(S(y5), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(0, y2), y3))), z3, Cons(0, Cons(0, y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(y2), y3), y4))), z3, Cons(0, Cons(S(y6), y7)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(S(y2))), y3))), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(0)), y2))), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Goto(S(y2)), y3))), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, Cons(S(0), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(IfGoto(S(0), y2), y3))), z3, Cons(0, Cons(S(0), y5)), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), z5)) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(Right, y4))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Right, I(Right, y2))), z3, Cons(0, Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), z3, Cons(0, z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(y3, y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(0, y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, z4), I(y4, I(Left, I(Goto(0), y5))))) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(y3), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Goto(0), y2)), Cons(y3, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Cons(y4, y5)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Cons(y4, y5)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Write(y2), y3))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Write(y2), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(0, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(0, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(S(y4), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(0, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(0, y2), y3))), Cons(0, y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(S(y5)), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(S(y5)), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(y2), y3), y4))), Cons(S(y5), y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(S(y2))), y3))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y2))), Cons(y3, y4), Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(0)), y2))), Cons(y3, y4), Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(0, z4), I(y7, y8)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Goto(S(y2)), y3))), Cons(y4, y5), Cons(0, z4), I(y7, y8))) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(S(y2)), y3), y4))), Cons(S(0), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(S(y4)), y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(IfGoto(S(0), y2), y3))), Cons(S(0), y4), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(0, Nil), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(Left, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(y3, Nil), Cons(0, z4), I(y5, I(Left, y6)))) TURING(I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(y3), Nil), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Left, I(Left, y2))), Cons(S(y3), Nil), Cons(0, 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I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(S(y3)), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(IfGoto(S(y3), y4), y5))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(S(y3))), y4))), z3, Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(S(y2)), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(IfGoto(S(0), y3), y4))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(IfGoto(S(0), y2), 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c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Right, y3)))), z3, Cons(0, Cons(y5, y6)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Left, y3)))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Left, y3)))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Right, I(Write(y3), y4)))), z3, Cons(0, Cons(y6, y7)), z5) -> c6(TURING[ITE](False, 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TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(0), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Goto(0), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(y3, y4)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(y3, y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(0, y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(0, y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), 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Nil, Cons(0, Cons(S(S(y3)), y4)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), Nil, Cons(0, Cons(S(0), y3)), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Goto(0), y3))), z3, Cons(0, z4), I(Goto(0), y6))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Goto(0), y2))), z3, Cons(0, z4), I(Goto(0), y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(0), y3))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Cons(y4, Cons(y5, y6)), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Write(y3), y4)))), Cons(y5, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(S(y3), y4), y5)))), Cons(0, y6), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(IfGoto(0, y3), y4)))), Cons(S(y5), y6), Cons(0, z4), z5)) 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I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(Goto(0), y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(Goto(0), y7))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(y8, y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(Goto(0), y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(y4, y5), Cons(0, z4), I(y7, I(Goto(0), y8)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Cons(0, y4), Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, 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y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(y4), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(S(y4)), y5)), I(Goto(S(0)), I(Goto(S(y6)), y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Goto(S(y2)), y3))), Nil, Cons(0, Cons(S(0), y4)), I(Goto(S(0)), I(Goto(S(y5)), y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Goto(S(y3)), y4))), Cons(y5, y6), Cons(0, z4), I(Goto(S(0)), I(Goto(S(y8)), y9)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(y2)), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, y3))), Nil, Cons(0, z4), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, y2))), Nil, Cons(0, z4), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, y2))), Nil, Cons(0, Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Goto(0), y3)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Goto(0), y2)))), Nil, Cons(0, z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(0), I(Left, I(Left, I(Goto(0), y2))))), Nil, Cons(0, z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(S(y2))), I(Left, I(y3, y4)))), Nil, Cons(0, z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(S(0)), I(Left, I(y2, y3)))), Nil, Cons(0, z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(Write(y2), I(Left, I(Left, y3)))), Nil, Cons(0, z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, 0), y2)), z3, Cons(0, z4), z5)) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(S(y2))), y3)), z3, Cons(0, z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(0)), y2)), z3, Cons(0, z4), I(y5, y6))) TURING(I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(S(z0), z1), I(IfGoto(0, S(y2)), y3)), z3, Cons(0, z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(0, y1), y2)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(S(y5)), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(S(S(y1))), y2)), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(S(y1)), y2), y3)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), y1), y2)), z2, Cons(S(S(y4)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(z3), z4), I(y4, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(S(y2)), z4), z5)) TURING(I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Left, y1)), Nil, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Cons(y4, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Left, y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Write(y1), y2))), z2, Cons(S(z3), Cons(y5, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(0, y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(S(y5), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(0, y1), y2))), z2, Cons(S(z3), Cons(0, y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(0), y1))), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(S(y6)), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(y1), y2), y3))), z2, Cons(S(z3), Cons(S(y6), y7)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(S(y1))), y2))), z2, Cons(S(z3), z4), I(y6, I(y7, y8)))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(0)), y1))), z2, Cons(S(z3), z4), I(y5, y6))) TURING(I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Goto(S(y1)), y2))), z2, Cons(S(z3), z4), I(y6, y7))) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(S(y1)), y2), y3))), z2, Cons(S(z3), Cons(S(0), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(S(y5)), y6)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(IfGoto(S(0), y1), y2))), z2, Cons(S(z3), Cons(S(0), y5)), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), z5)) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(Right, y4))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Right, I(Right, y1))), z2, Cons(S(z3), Nil), I(y4, I(Right, y5)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), z5)) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(Goto(0), y5))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(z3), z4), I(y5, I(Goto(0), y6)))) TURING(I(IfGoto(0, z0), I(Goto(0), y1)), z2, Cons(S(S(y3)), z4), z5) -> 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I(Write(S(0)), I(Left, y1))), Nil, Cons(S(z3), z4), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(y3, y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(0, y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(y3), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(S(y3)), y4)), I(Left, y5))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, y1))), Nil, Cons(S(z3), Cons(S(0), y3)), I(Left, y4))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Goto(0), y2)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y5)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Goto(0), y1)))), Nil, Cons(S(z3), z4), I(Left, I(Goto(0), y4)))) TURING(I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4)))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(0), I(Left, I(Left, I(Goto(0), y1))))), Nil, Cons(S(z3), z4), I(Left, I(Left, I(Goto(0), y4))))) TURING(I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(S(y1))), I(Left, I(y2, y3)))), Nil, Cons(S(z3), z4), I(Left, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(S(0)), I(Left, I(y1, y2)))), Nil, Cons(S(z3), z4), I(Left, I(y5, y6)))) TURING(I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(Write(y1), I(Left, I(Left, y2)))), Nil, Cons(S(z3), z4), I(Left, I(Left, y5)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), 0), y1)), z2, Cons(S(0), z4), z5)) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7))) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(S(y1))), y2)), z2, Cons(S(0), z4), I(y5, I(y6, y7)))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(0)), y1)), z2, Cons(S(0), z4), I(y4, y5))) TURING(I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6)) -> c6(TURING[ITE](False, I(IfGoto(0, z0), I(IfGoto(S(0), S(y1)), y2)), z2, Cons(S(0), z4), I(y5, y6))) K tuples: TURING(I(Goto(S(z0)), z1), x2, Cons(x0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, x3, I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(0, x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(x3), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(0), x4), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(Right, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Right, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Cons(0, x1), Nil, I(x2, I(Right, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Right, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(Left, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Left, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(x3, x4))) -> c7(LOOKUP(S(z0), I(x2, I(x3, x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, x1), I(x2, I(Left, I(Goto(S(z0)), z1)))) -> c7(LOOKUP(S(z0), I(x2, I(Left, I(Goto(S(z0)), z1))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(z4, z5)) -> c7(LOOKUP(S(z0), I(z4, z5))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(S(x0))), x1), Cons(x3, x2), x4, I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), Cons(x2, x1), x3, I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(x0)), x1), Cons(x3, x2), x4, I(x5, x6)) -> c7(LOOKUP(S(x0), I(x5, x6))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x4, x5)), x1, x2, I(Goto(S(z0)), I(x4, x5))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x4, x5)))) TURING(I(Goto(S(z0)), I(Goto(0), x0)), x1, x2, I(Goto(S(z0)), I(Goto(0), x0))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Goto(0), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Cons(0, x1), Nil, I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Right, I(Goto(0), x0))), Cons(0, x1), Nil, I(Goto(S(z0)), I(Right, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Right, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), I(x3, x4)), Nil, Cons(0, x1), I(Goto(S(z0)), I(x3, x4))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(x3, x4)))) TURING(I(Goto(S(z0)), I(Left, I(Goto(0), x0))), Nil, Cons(0, x1), I(Goto(S(z0)), I(Left, I(Goto(0), x0)))) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), I(Left, I(Goto(0), x0))))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(z0)), z1)) -> c7(LOOKUP(S(z0), I(Goto(S(z0)), z1))) TURING(I(Goto(S(z0)), z1), x2, Cons(0, x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x3, Cons(S(S(x4)), x5), I(x6, I(x7, x8))) -> c7(LOOKUP(S(z0), I(x6, I(x7, x8)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(0), x3), I(x4, I(x5, x6))) -> c7(LOOKUP(S(z0), I(x4, I(x5, x6)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x2, Cons(S(S(x3)), x4), I(x5, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x5, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(S(x0))), x1), x3, Cons(x2, x4), I(x5, I(x6, x7))) -> c7(LOOKUP(S(S(x0)), I(x5, I(x6, x7)))) TURING(I(Goto(S(0)), x0), x2, Cons(x1, x3), I(x4, x5)) -> c7(LOOKUP(S(0), I(x4, x5))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x5), x1, x2, I(x3, I(Goto(S(z0)), x5))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), x5)))) TURING(I(Goto(S(0)), x0), x1, x2, I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Cons(0, x1), Nil, I(Right, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Right, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Cons(0, x1), Nil, I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), Nil, Cons(0, x1), I(Left, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(Left, I(Goto(S(0)), x0)))) TURING(I(Goto(S(z0)), x4), Nil, Cons(0, x1), I(x2, I(Goto(S(z0)), x4))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), x4)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(x3, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x3, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(x2, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x2, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(S(x2)), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(0), x2), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(x4, I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(x4, I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(x2, x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), x2, x3, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), x1, Cons(S(x2), x3), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(x1, x2)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(0, Cons(0, x1)), Nil, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Cons(0, x2), Nil, I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(x1, x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(0, x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), x1), Nil, Cons(0, x2), I(Goto(S(0)), I(Goto(S(z0)), x1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), x1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(x1), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(S(x1)), x2)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Nil, Cons(0, Cons(S(0), x1)), I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(z0)), z1), Cons(x1, x2), x3, I(Goto(S(0)), I(Goto(S(z0)), z1))) -> c7(LOOKUP(S(z0), I(Goto(S(0)), I(Goto(S(z0)), z1)))) TURING(I(Goto(S(0)), x0), x1, Cons(0, x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(S(x2)), x3), I(x4, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x4, I(Goto(S(0)), x0)))) TURING(I(Goto(S(0)), x0), x1, Cons(S(0), x2), I(x3, I(Goto(S(0)), x0))) -> c7(LOOKUP(S(0), I(x3, I(Goto(S(0)), x0)))) TURING(I(IfGoto(S(S(y1)), z1), z2), z3, Cons(S(S(y0)), z5), z6) -> c6(!EQ'(S(S(y0)), S(S(y1)))) Defined Rule Symbols: lookup_2, !EQ_2 Defined Pair Symbols: LOOKUP_2, TURING_4, TURING[ITE]_5, !EQ'_2 Compound Symbols: c16, c6_2, c7_2, c6_1, c5_1, c9_1, c11_1, c4_2, c8_1, c4_1, c10_1, c7_1, c12_1, c15_1, c_1