KILLED proof of input_wiCfnTpMmW.trs # AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 57 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxRelTRS (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) typed CpxTrs (13) OrderProof [LOWER BOUND(ID), 22 ms] (14) typed CpxTrs (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 19 ms] (28) CpxRNTS (29) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 4 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 107.9 s] (34) CpxRNTS (35) CompletionProof [UPPER BOUND(ID), 28 ms] (36) CpxTypedWeightedCompleteTrs (37) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 18 ms] (46) CdtProblem (47) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxRelTRS (49) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (50) CpxTRS (51) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CpxWeightedTrs (53) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CpxTypedWeightedTrs (55) CompletionProof [UPPER BOUND(ID), 0 ms] (56) CpxTypedWeightedCompleteTrs (57) NarrowingProof [BOTH BOUNDS(ID, ID), 19 ms] (58) CpxTypedWeightedCompleteTrs (59) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms] (60) CpxRNTS (61) InliningProof [UPPER BOUND(ID), 1138 ms] (62) CpxRNTS (63) SimplificationProof [BOTH BOUNDS(ID, ID), 42 ms] (64) CpxRNTS (65) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CpxRNTS (67) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (68) CpxRNTS (69) IntTrsBoundProof [UPPER BOUND(ID), 88.2 s] (70) CpxRNTS (71) CompletionProof [UPPER BOUND(ID), 0 ms] (72) CpxTypedWeightedCompleteTrs (73) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms] (74) CpxRNTS (75) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 254 ms] (76) CdtProblem (77) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 78 ms] (78) CdtProblem (79) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 71 ms] (80) CdtProblem (81) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 64 ms] (82) CdtProblem (83) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 40 ms] (84) CdtProblem (85) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 1100 ms] (88) CdtProblem (89) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (122) CdtProblem (123) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (132) CdtProblem (133) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (138) CdtProblem (139) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms] (140) CdtProblem (141) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (172) CdtProblem (173) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (178) CdtProblem (179) CdtInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem (187) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (188) CdtProblem (189) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (192) CdtProblem (193) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (194) CdtProblem (195) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 9 ms] (196) CdtProblem (197) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (200) CdtProblem (201) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (202) CdtProblem (203) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (204) CdtProblem (205) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 8 ms] (206) CdtProblem (207) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 2 ms] (208) CdtProblem (209) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (210) CdtProblem (211) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (212) CdtProblem (213) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (214) CdtProblem (215) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 4 ms] (216) CdtProblem ---------------------------------------- (0) 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: start(i) -> busy(F, closed, stop, false, false, false, i) busy(BF, d, stop, b1, b2, b3, i) -> incorrect busy(FS, d, stop, b1, b2, b3, i) -> incorrect busy(fl, open, up, b1, b2, b3, i) -> incorrect busy(fl, open, down, b1, b2, b3, i) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) or(true, b) -> true or(false, b) -> b S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) 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: start(i) -> busy(F, closed, stop, false, false, false, i) busy(BF, d, stop, b1, b2, b3, i) -> incorrect busy(FS, d, stop, b1, b2, b3, i) -> incorrect busy(fl, open, up, b1, b2, b3, i) -> incorrect busy(fl, open, down, b1, b2, b3, i) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) or(true, b) -> true or(false, b) -> b S is empty. 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: start(i) -> busy(F, closed, stop, false, false, false, i) busy(BF, d, stop, b1, b2, b3, i) -> incorrect busy(FS, d, stop, b1, b2, b3, i) -> incorrect busy(fl, open, up, b1, b2, b3, i) -> incorrect busy(fl, open, down, b1, b2, b3, i) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) or(true, b) -> true or(false, b) -> b S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Tuples: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 S tuples: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 K tuples:none Defined Rule Symbols: start_1, busy_7, idle_7, or_2 Defined Pair Symbols: START_1, BUSY_7, IDLE_7, OR_2 Compound Symbols: c_1, c1, c2, c3, c4, c5, c6, c7, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_2, c39_2, c40_2, c41, c42 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 The (relative) TRS S consists of the following rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (10) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 The (relative) TRS S consists of the following rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (11) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (12) Obligation: Innermost TRS: Rules: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Types: START :: empty:newbuttons -> c c :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c BUSY :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S c1 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 FS :: F:BF:FS:B:S c2 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 open :: closed:open up :: stop:up:down c3 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 down :: stop:up:down c4 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 B :: F:BF:FS:B:S empty :: empty:newbuttons c5 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c6 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 S :: F:BF:FS:B:S c7 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons c8 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 IDLE :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> c37:c38:c39:c40 c9 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c10 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c11 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c12 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c13 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 true :: false:true c14 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c15 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c16 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c17 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c18 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c19 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c20 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c21 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c22 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c23 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c24 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c25 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c26 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c27 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c28 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c29 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c30 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c31 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c32 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c33 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c34 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c35 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c36 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c37 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15: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 c38 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 or :: false:true -> false:true -> false:true OR :: false:true -> false:true -> c41:c42 c39 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 c40 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 c41 :: c41:c42 c42 :: c41:c42 start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct incorrect :: incorrect:correct correct :: incorrect:correct idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct hole_c1_43 :: c hole_empty:newbuttons2_43 :: empty:newbuttons hole_c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_43 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 hole_F:BF:FS:B:S4_43 :: F:BF:FS:B:S hole_closed:open5_43 :: closed:open hole_stop:up:down6_43 :: stop:up:down hole_false:true7_43 :: false:true hole_c37:c38:c39:c408_43 :: c37:c38:c39:c40 hole_c41:c429_43 :: c41:c42 hole_incorrect:correct10_43 :: incorrect:correct gen_empty:newbuttons11_43 :: Nat -> empty:newbuttons ---------------------------------------- (13) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: BUSY, IDLE, busy, idle They will be analysed ascendingly in the following order: BUSY = IDLE busy = idle ---------------------------------------- (14) Obligation: Innermost TRS: Rules: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Types: START :: empty:newbuttons -> c c :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c BUSY :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S c1 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 FS :: F:BF:FS:B:S c2 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 open :: closed:open up :: stop:up:down c3 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 down :: stop:up:down c4 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 B :: F:BF:FS:B:S empty :: empty:newbuttons c5 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c6 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 S :: F:BF:FS:B:S c7 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons c8 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 IDLE :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> c37:c38:c39:c40 c9 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c10 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c11 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c12 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c13 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 true :: false:true c14 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c15 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c16 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c17 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c18 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c19 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c20 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c21 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c22 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c23 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c24 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c25 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c26 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c27 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c28 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c29 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c30 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c31 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c32 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c33 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c34 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c35 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c36 :: c37:c38:c39:c40 -> c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c37 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15: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 c38 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 or :: false:true -> false:true -> false:true OR :: false:true -> false:true -> c41:c42 c39 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 c40 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 -> c41:c42 -> c37:c38:c39:c40 c41 :: c41:c42 c42 :: c41:c42 start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct incorrect :: incorrect:correct correct :: incorrect:correct idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct hole_c1_43 :: c hole_empty:newbuttons2_43 :: empty:newbuttons hole_c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c363_43 :: c1:c2:c3:c4:c5:c6:c7:c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 hole_F:BF:FS:B:S4_43 :: F:BF:FS:B:S hole_closed:open5_43 :: closed:open hole_stop:up:down6_43 :: stop:up:down hole_false:true7_43 :: false:true hole_c37:c38:c39:c408_43 :: c37:c38:c39:c40 hole_c41:c429_43 :: c41:c42 hole_incorrect:correct10_43 :: incorrect:correct gen_empty:newbuttons11_43 :: Nat -> empty:newbuttons Generator Equations: gen_empty:newbuttons11_43(0) <=> empty gen_empty:newbuttons11_43(+(x, 1)) <=> newbuttons(false, false, false, gen_empty:newbuttons11_43(x)) The following defined symbols remain to be analysed: idle, BUSY, IDLE, busy They will be analysed ascendingly in the following order: BUSY = IDLE busy = idle ---------------------------------------- (15) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (16) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 The (relative) TRS S consists of the following rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) 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: start(i) -> busy(F, closed, stop, false, false, false, i) [1] busy(BF, d, stop, b1, b2, b3, i) -> incorrect [1] busy(FS, d, stop, b1, b2, b3, i) -> incorrect [1] busy(fl, open, up, b1, b2, b3, i) -> incorrect [1] busy(fl, open, down, b1, b2, b3, i) -> incorrect [1] busy(B, closed, stop, false, false, false, empty) -> correct [1] busy(F, closed, stop, false, false, false, empty) -> correct [1] busy(S, closed, stop, false, false, false, empty) -> correct [1] busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) [1] busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) [1] busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) [1] busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) [1] busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) [1] busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) [1] busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) [1] busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) [1] busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) [1] busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) [1] busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) [1] busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) [1] busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) [1] busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) [1] busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) [1] busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) [1] busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) [1] busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) [1] busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) [1] busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) [1] busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) [1] busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) [1] busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) [1] busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) [1] idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) [1] idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) [1] or(true, b) -> true [1] or(false, b) -> b [1] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: start(i) -> busy(F, closed, stop, false, false, false, i) [1] busy(BF, d, stop, b1, b2, b3, i) -> incorrect [1] busy(FS, d, stop, b1, b2, b3, i) -> incorrect [1] busy(fl, open, up, b1, b2, b3, i) -> incorrect [1] busy(fl, open, down, b1, b2, b3, i) -> incorrect [1] busy(B, closed, stop, false, false, false, empty) -> correct [1] busy(F, closed, stop, false, false, false, empty) -> correct [1] busy(S, closed, stop, false, false, false, empty) -> correct [1] busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) [1] busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) [1] busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) [1] busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) [1] busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) [1] busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) [1] busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) [1] busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) [1] busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) [1] busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) [1] busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) [1] busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) [1] busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) [1] busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) [1] busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) [1] busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) [1] busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) [1] busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) [1] busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) [1] busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) [1] busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) [1] busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) [1] busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) [1] busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) [1] idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) [1] idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) [1] or(true, b) -> true [1] or(false, b) -> b [1] The TRS has the following type information: start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S incorrect :: incorrect:correct FS :: F:BF:FS:B:S open :: closed:open up :: stop:up:down down :: stop:up:down B :: F:BF:FS:B:S empty :: empty:newbuttons correct :: incorrect:correct S :: F:BF:FS:B:S newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct true :: false:true or :: false:true -> false:true -> false:true Rewrite Strategy: INNERMOST ---------------------------------------- (21) 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: start_1 busy_7 idle_7 (c) The following functions are completely defined: or_2 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (22) 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: start(i) -> busy(F, closed, stop, false, false, false, i) [1] busy(BF, d, stop, b1, b2, b3, i) -> incorrect [1] busy(FS, d, stop, b1, b2, b3, i) -> incorrect [1] busy(fl, open, up, b1, b2, b3, i) -> incorrect [1] busy(fl, open, down, b1, b2, b3, i) -> incorrect [1] busy(B, closed, stop, false, false, false, empty) -> correct [1] busy(F, closed, stop, false, false, false, empty) -> correct [1] busy(S, closed, stop, false, false, false, empty) -> correct [1] busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) [1] busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) [1] busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) [1] busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) [1] busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) [1] busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) [1] busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) [1] busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) [1] busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) [1] busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) [1] busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) [1] busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) [1] busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) [1] busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) [1] busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) [1] busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) [1] busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) [1] busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) [1] busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) [1] busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) [1] busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) [1] busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) [1] busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) [1] busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) [1] idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) [1] idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) [1] or(true, b) -> true [1] or(false, b) -> b [1] The TRS has the following type information: start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S incorrect :: incorrect:correct FS :: F:BF:FS:B:S open :: closed:open up :: stop:up:down down :: stop:up:down B :: F:BF:FS:B:S empty :: empty:newbuttons correct :: incorrect:correct S :: F:BF:FS:B:S newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct true :: false:true or :: false:true -> false:true -> false:true Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (24) 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: start(i) -> busy(F, closed, stop, false, false, false, i) [1] busy(BF, d, stop, b1, b2, b3, i) -> incorrect [1] busy(FS, d, stop, b1, b2, b3, i) -> incorrect [1] busy(fl, open, up, b1, b2, b3, i) -> incorrect [1] busy(fl, open, down, b1, b2, b3, i) -> incorrect [1] busy(B, closed, stop, false, false, false, empty) -> correct [1] busy(F, closed, stop, false, false, false, empty) -> correct [1] busy(S, closed, stop, false, false, false, empty) -> correct [1] busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) [1] busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) [1] busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) [1] busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) [1] busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) [1] busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) [1] busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) [1] busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) [1] busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) [1] busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) [1] busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) [1] busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) [1] busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) [1] busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) [1] busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) [1] busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) [1] busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) [1] busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) [1] busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) [1] busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) [1] busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) [1] busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) [1] busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) [1] busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) [1] idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) [1] idle(fl, d, m, true, true, true, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, true, true, true, i) [4] idle(fl, d, m, true, true, false, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, true, true, i3, i) [4] idle(fl, d, m, true, false, true, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, true, i2, true, i) [4] idle(fl, d, m, true, false, false, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, true, i2, i3, i) [4] idle(fl, d, m, false, true, true, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, i1, true, true, i) [4] idle(fl, d, m, false, true, false, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, i1, true, i3, i) [4] idle(fl, d, m, false, false, true, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, i1, i2, true, i) [4] idle(fl, d, m, false, false, false, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, i1, i2, i3, i) [4] or(true, b) -> true [1] or(false, b) -> b [1] The TRS has the following type information: start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S incorrect :: incorrect:correct FS :: F:BF:FS:B:S open :: closed:open up :: stop:up:down down :: stop:up:down B :: F:BF:FS:B:S empty :: empty:newbuttons correct :: incorrect:correct S :: F:BF:FS:B:S newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct true :: false:true or :: false:true -> false:true -> false:true Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: F => 2 closed => 0 stop => 1 false => 0 BF => 1 incorrect => 1 FS => 3 open => 1 up => 2 down => 0 B => 0 empty => 0 correct => 0 S => 4 true => 1 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, b1, b2, 0, i) :|: z' = d, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, b1, b2, b3, i) :|: b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, b3, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z = 4, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, 1, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, 0, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z3 = 0, z4 = i, i >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, b1, 1, 0, i) :|: z1 = b1, b1 >= 0, z2 = 1, z3 = 0, z4 = i, i >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, i) :|: z2 = 0, z3 = 0, z1 = 1, z4 = i, i >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, b1, 0, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, b1, b2, 0, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z3 = 0, z4 = i, i >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, b1, 0, b3, i) :|: z = 2, z' = d, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, b1, b2, b3, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, i) :|: z = 2, z1 = 0, z2 = 0, z4 = i, i >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 1, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 1, b3, i) :|: z = 2, z'' = 0, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 0, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z' = 1, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, b3, i) :|: z = 2, z2 = 0, z1 = 1, z4 = i, i >= 0, z3 = b3, z'' = 1, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, b2, b3, i) :|: b2 >= 0, z1 = 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, b1, 0, b3, i) :|: z = 2, z'' = 0, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, b2, b3, i) :|: z' = d, b2 >= 0, z2 = b2, z1 = 1, z4 = i, i >= 0, d >= 0, z = 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, b3, i) :|: z1 = 0, z2 = 1, z4 = i, i >= 0, z = 0, z3 = b3, z'' = 1, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, i) :|: z1 = 0, z2 = 0, z4 = i, i >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, b2, b3, i) :|: b2 >= 0, z2 = b2, z1 = 1, z4 = i, i >= 0, z'' = 2, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, b2, b3, i) :|: b2 >= 0, z1 = 0, z2 = b2, z4 = i, i >= 0, z' = 1, z = 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z' = d, b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z' = d, b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, fl >= 0, z4 = i, i >= 0, z = fl, z' = 1, z'' = 2, z3 = b3, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, fl >= 0, z4 = i, i >= 0, z = fl, z' = 1, z3 = b3, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(fl, d, m, b1, b2, b3, 0) :|: z1 = b1, b1 >= 0, z2 = b2, z = fl, d >= 0, z3 = b3, b3 >= 0, z' = d, b2 >= 0, z4 = 0, fl >= 0, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, i1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, i >= 0, z = fl, d >= 0, i2 >= 0, i3 >= 0, z' = d, z1 = 0, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, i1, i2, 1, i) :|: i1 >= 0, z2 = 0, i >= 0, z = fl, d >= 0, z3 = 1, i2 >= 0, i3 >= 0, z' = d, z1 = 0, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, i1, 1, i3, i) :|: i1 >= 0, z3 = 0, i >= 0, z = fl, d >= 0, i2 >= 0, i3 >= 0, z' = d, z1 = 0, z2 = 1, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, i1, 1, 1, i) :|: i1 >= 0, i >= 0, z = fl, d >= 0, z3 = 1, i2 >= 0, i3 >= 0, z' = d, z1 = 0, z2 = 1, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, 1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, z1 = 1, i >= 0, z = fl, d >= 0, i2 >= 0, i3 >= 0, z' = d, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, 1, i2, 1, i) :|: i1 >= 0, z2 = 0, z1 = 1, i >= 0, z = fl, d >= 0, z3 = 1, i2 >= 0, i3 >= 0, z' = d, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, 1, 1, i3, i) :|: i1 >= 0, z3 = 0, z1 = 1, i >= 0, z = fl, d >= 0, i2 >= 0, i3 >= 0, z' = d, z2 = 1, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(fl, d, m, 1, 1, 1, i) :|: i1 >= 0, z1 = 1, i >= 0, z = fl, d >= 0, z3 = 1, i2 >= 0, i3 >= 0, z' = d, z2 = 1, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 or(z, z') -{ 1 }-> b :|: b >= 0, z' = b, z = 0 or(z, z') -{ 1 }-> 1 :|: b >= 0, z = 1, z' = b start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, i) :|: z = i, i >= 0 ---------------------------------------- (27) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z' >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z'' = 2, z = 4, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 1, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, z1, 1, 0, z4) :|: z1 >= 0, z2 = 1, z3 = 0, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, z4) :|: z2 = 0, z3 = 0, z1 = 1, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, z1, z2, 0, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, z4) :|: z = 2, z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z' = 1, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, z3, z4) :|: z = 2, z2 = 0, z1 = 1, z4 >= 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, z1, 0, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z' >= 0, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, z3, z4) :|: z1 = 0, z2 = 1, z4 >= 0, z = 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, z4) :|: z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z' = 1, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z'' = 2, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, 1, i) :|: i1 >= 0, z2 = 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, i3, i) :|: i1 >= 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, 1, i) :|: i1 >= 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(z, z', z'', z1, z2, z3, 0) :|: z1 >= 0, z' >= 0, z3 >= 0, z2 >= 0, z4 = 0, z >= 0, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, 1, i) :|: i1 >= 0, z2 = 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, i3, i) :|: i1 >= 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, 1, i) :|: i1 >= 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 or(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 1 start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, z) :|: z >= 0 ---------------------------------------- (29) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { idle, busy } { or } { start } ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z' >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z'' = 2, z = 4, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 1, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, z1, 1, 0, z4) :|: z1 >= 0, z2 = 1, z3 = 0, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, z4) :|: z2 = 0, z3 = 0, z1 = 1, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, z1, z2, 0, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, z4) :|: z = 2, z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z' = 1, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, z3, z4) :|: z = 2, z2 = 0, z1 = 1, z4 >= 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, z1, 0, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z' >= 0, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, z3, z4) :|: z1 = 0, z2 = 1, z4 >= 0, z = 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, z4) :|: z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z' = 1, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z'' = 2, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, 1, i) :|: i1 >= 0, z2 = 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, i3, i) :|: i1 >= 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, 1, i) :|: i1 >= 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(z, z', z'', z1, z2, z3, 0) :|: z1 >= 0, z' >= 0, z3 >= 0, z2 >= 0, z4 = 0, z >= 0, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, 1, i) :|: i1 >= 0, z2 = 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, i3, i) :|: i1 >= 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, 1, i) :|: i1 >= 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 or(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 1 start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, z) :|: z >= 0 Function symbols to be analyzed: {idle,busy}, {or}, {start} ---------------------------------------- (31) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z' >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z'' = 2, z = 4, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 1, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, z1, 1, 0, z4) :|: z1 >= 0, z2 = 1, z3 = 0, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, z4) :|: z2 = 0, z3 = 0, z1 = 1, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, z1, z2, 0, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, z4) :|: z = 2, z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z' = 1, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, z3, z4) :|: z = 2, z2 = 0, z1 = 1, z4 >= 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, z1, 0, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z' >= 0, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, z3, z4) :|: z1 = 0, z2 = 1, z4 >= 0, z = 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, z4) :|: z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z' = 1, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z'' = 2, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, 1, i) :|: i1 >= 0, z2 = 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, i3, i) :|: i1 >= 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, 1, i) :|: i1 >= 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(z, z', z'', z1, z2, z3, 0) :|: z1 >= 0, z' >= 0, z3 >= 0, z2 >= 0, z4 = 0, z >= 0, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, 1, i) :|: i1 >= 0, z2 = 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, i3, i) :|: i1 >= 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, 1, i) :|: i1 >= 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 or(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 1 start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, z) :|: z >= 0 Function symbols to be analyzed: {idle,busy}, {or}, {start} ---------------------------------------- (33) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: idle after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 4 Computed SIZE bound using KoAT for: busy after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 4 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z' >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z4 >= 0, z'' = 2, z = 4, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 1, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, z1, z2, 0, z4) :|: z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, z1, 1, 0, z4) :|: z1 >= 0, z2 = 1, z3 = 0, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, z4) :|: z2 = 0, z3 = 0, z1 = 1, z4 >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, z1, z2, 0, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z3 = 0, z4 >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, z1, z2, z3, z4) :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, z4) :|: z = 2, z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z1 >= 0, z2 = 1, z4 >= 0, z'' = 2, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 1, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, z1, 0, z3, z4) :|: z = 2, z1 >= 0, z2 = 0, z4 >= 0, z' = 1, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, z3, z4) :|: z = 2, z2 = 0, z1 = 1, z4 >= 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, z1, 0, z3, z4) :|: z = 2, z'' = 0, z1 >= 0, z2 = 0, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z' >= 0, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, z3, z4) :|: z1 = 0, z2 = 1, z4 >= 0, z = 0, z'' = 1, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, z4) :|: z1 = 0, z2 = 0, z4 >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z4 >= 0, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, z2, z3, z4) :|: z2 >= 0, z1 = 1, z4 >= 0, z'' = 2, z = 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, z2, z3, z4) :|: z2 >= 0, z1 = 0, z4 >= 0, z' = 1, z = 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, z1, z2, z3, z4) :|: z'' = 0, z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' = 0, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z = 1, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z = 3, z1 >= 0, z4 >= 0, z' >= 0, z'' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z'' = 2, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, z2 >= 0, z1 >= 0, z >= 0, z4 >= 0, z' = 1, z3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, i2, 1, i) :|: i1 >= 0, z2 = 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, i3, i) :|: i1 >= 0, z3 = 0, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', i1, 1, 1, i) :|: i1 >= 0, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z1 = 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(z, z', z'', z1, z2, z3, 0) :|: z1 >= 0, z' >= 0, z3 >= 0, z2 >= 0, z4 = 0, z >= 0, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, i3, i) :|: i1 >= 0, z2 = 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, i2, 1, i) :|: i1 >= 0, z2 = 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, i3, i) :|: i1 >= 0, z3 = 0, z1 = 1, i >= 0, z' >= 0, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 4 }-> busy(z, z', z'', 1, 1, 1, i) :|: i1 >= 0, z1 = 1, i >= 0, z' >= 0, z3 = 1, i2 >= 0, i3 >= 0, z2 = 1, z >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' >= 0 or(z, z') -{ 1 }-> z' :|: z' >= 0, z = 0 or(z, z') -{ 1 }-> 1 :|: z' >= 0, z = 1 start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, z) :|: z >= 0 Function symbols to be analyzed: {idle,busy}, {or}, {start} Previous analysis results are: idle: runtime: ?, size: O(1) [4] busy: runtime: ?, size: O(1) [4] ---------------------------------------- (35) 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: none And the following fresh constants: none ---------------------------------------- (36) 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: start(i) -> busy(F, closed, stop, false, false, false, i) [1] busy(BF, d, stop, b1, b2, b3, i) -> incorrect [1] busy(FS, d, stop, b1, b2, b3, i) -> incorrect [1] busy(fl, open, up, b1, b2, b3, i) -> incorrect [1] busy(fl, open, down, b1, b2, b3, i) -> incorrect [1] busy(B, closed, stop, false, false, false, empty) -> correct [1] busy(F, closed, stop, false, false, false, empty) -> correct [1] busy(S, closed, stop, false, false, false, empty) -> correct [1] busy(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(B, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(F, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) -> idle(S, closed, stop, false, false, false, newbuttons(i1, i2, i3, i)) [1] busy(B, open, stop, false, b2, b3, i) -> idle(B, closed, stop, false, b2, b3, i) [1] busy(F, open, stop, b1, false, b3, i) -> idle(F, closed, stop, b1, false, b3, i) [1] busy(S, open, stop, b1, b2, false, i) -> idle(S, closed, stop, b1, b2, false, i) [1] busy(B, d, stop, true, b2, b3, i) -> idle(B, open, stop, false, b2, b3, i) [1] busy(F, d, stop, b1, true, b3, i) -> idle(F, open, stop, b1, false, b3, i) [1] busy(S, d, stop, b1, b2, true, i) -> idle(S, open, stop, b1, b2, false, i) [1] busy(B, closed, down, b1, b2, b3, i) -> idle(B, closed, stop, b1, b2, b3, i) [1] busy(S, closed, up, b1, b2, b3, i) -> idle(S, closed, stop, b1, b2, b3, i) [1] busy(B, closed, up, true, b2, b3, i) -> idle(B, closed, stop, true, b2, b3, i) [1] busy(F, closed, up, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(F, closed, down, b1, true, b3, i) -> idle(F, closed, stop, b1, true, b3, i) [1] busy(S, closed, down, b1, b2, true, i) -> idle(S, closed, stop, b1, b2, true, i) [1] busy(B, closed, up, false, b2, b3, i) -> idle(BF, closed, up, false, b2, b3, i) [1] busy(F, closed, up, b1, false, b3, i) -> idle(FS, closed, up, b1, false, b3, i) [1] busy(F, closed, down, b1, false, b3, i) -> idle(BF, closed, down, b1, false, b3, i) [1] busy(S, closed, down, b1, b2, false, i) -> idle(FS, closed, down, b1, b2, false, i) [1] busy(BF, closed, up, b1, b2, b3, i) -> idle(F, closed, up, b1, b2, b3, i) [1] busy(BF, closed, down, b1, b2, b3, i) -> idle(B, closed, down, b1, b2, b3, i) [1] busy(FS, closed, up, b1, b2, b3, i) -> idle(S, closed, up, b1, b2, b3, i) [1] busy(FS, closed, down, b1, b2, b3, i) -> idle(F, closed, down, b1, b2, b3, i) [1] busy(B, closed, stop, false, true, b3, i) -> idle(B, closed, up, false, true, b3, i) [1] busy(B, closed, stop, false, false, true, i) -> idle(B, closed, up, false, false, true, i) [1] busy(F, closed, stop, true, false, b3, i) -> idle(F, closed, down, true, false, b3, i) [1] busy(F, closed, stop, false, false, true, i) -> idle(F, closed, up, false, false, true, i) [1] busy(S, closed, stop, b1, true, false, i) -> idle(S, closed, down, b1, true, false, i) [1] busy(S, closed, stop, true, false, false, i) -> idle(S, closed, down, true, false, false, i) [1] idle(fl, d, m, b1, b2, b3, empty) -> busy(fl, d, m, b1, b2, b3, empty) [1] idle(fl, d, m, b1, b2, b3, newbuttons(i1, i2, i3, i)) -> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) [1] or(true, b) -> true [1] or(false, b) -> b [1] The TRS has the following type information: start :: empty:newbuttons -> incorrect:correct busy :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct F :: F:BF:FS:B:S closed :: closed:open stop :: stop:up:down false :: false:true BF :: F:BF:FS:B:S incorrect :: incorrect:correct FS :: F:BF:FS:B:S open :: closed:open up :: stop:up:down down :: stop:up:down B :: F:BF:FS:B:S empty :: empty:newbuttons correct :: incorrect:correct S :: F:BF:FS:B:S newbuttons :: false:true -> false:true -> false:true -> empty:newbuttons -> empty:newbuttons idle :: F:BF:FS:B:S -> closed:open -> stop:up:down -> false:true -> false:true -> false:true -> empty:newbuttons -> incorrect:correct true :: false:true or :: false:true -> false:true -> false:true Rewrite Strategy: INNERMOST ---------------------------------------- (37) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: F => 2 closed => 0 stop => 1 false => 0 BF => 1 incorrect => 1 FS => 3 open => 1 up => 2 down => 0 B => 0 empty => 0 correct => 0 S => 4 true => 1 ---------------------------------------- (38) Obligation: Complexity RNTS consisting of the following rules: busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 1, 1, b1, b2, 0, i) :|: z' = d, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 2, b1, b2, b3, i) :|: b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, b3, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z = 4, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, 1, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z3 = 1, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, b1, b2, 0, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z3 = 0, z4 = i, i >= 0, z' = 1, z = 4, z'' = 1 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 4, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, b1, 1, 0, i) :|: z1 = b1, b1 >= 0, z2 = 1, z3 = 0, z4 = i, i >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(4, 0, 0, 1, 0, 0, i) :|: z2 = 0, z3 = 0, z1 = 1, z4 = i, i >= 0, z = 4, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 2, b1, 0, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(3, 0, 0, b1, b2, 0, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z3 = 0, z4 = i, i >= 0, z = 4, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 1, 1, b1, 0, b3, i) :|: z = 2, z' = d, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, b1, b2, b3, i) :|: b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 2, 0, 0, 1, i) :|: z = 2, z1 = 0, z2 = 0, z4 = i, i >= 0, z3 = 1, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 1, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, z'' = 2, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 1, b3, i) :|: z = 2, z'' = 0, z1 = b1, b1 >= 0, z2 = 1, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, b1, 0, b3, i) :|: z = 2, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z' = 1, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z = 2, z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(2, 0, 0, 1, 0, b3, i) :|: z = 2, z2 = 0, z1 = 1, z4 = i, i >= 0, z3 = b3, z'' = 1, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 2, 0, b2, b3, i) :|: b2 >= 0, z1 = 0, z2 = b2, z4 = i, i >= 0, z'' = 2, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(1, 0, 0, b1, 0, b3, i) :|: z = 2, z'' = 0, z1 = b1, b1 >= 0, z2 = 0, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 1, 1, 0, b2, b3, i) :|: z' = d, b2 >= 0, z2 = b2, z1 = 1, z4 = i, i >= 0, d >= 0, z = 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 1, b3, i) :|: z1 = 0, z2 = 1, z4 = i, i >= 0, z = 0, z3 = b3, z'' = 1, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 2, 0, 0, 1, i) :|: z1 = 0, z2 = 0, z4 = i, i >= 0, z3 = 1, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 1, b2, b3, i) :|: b2 >= 0, z2 = b2, z1 = 1, z4 = i, i >= 0, z'' = 2, z = 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, b2, b3, i) :|: b2 >= 0, z1 = 0, z2 = b2, z4 = i, i >= 0, z' = 1, z = 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 1, 0, 0, 0, 1 + i1 + i2 + i3 + i) :|: z1 = 0, i1 >= 0, z2 = 0, z3 = 0, z4 = 1 + i1 + i2 + i3 + i, i >= 0, z = 0, i2 >= 0, z'' = 1, z' = 0, i3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> idle(0, 0, 0, b1, b2, b3, i) :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, z3 = b3, z' = 0, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z' = d, b2 >= 0, z1 = b1, b1 >= 0, z = 1, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z' = d, b2 >= 0, z = 3, z1 = b1, b1 >= 0, z2 = b2, z4 = i, i >= 0, d >= 0, z3 = b3, z'' = 1, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, fl >= 0, z4 = i, i >= 0, z = fl, z' = 1, z'' = 2, z3 = b3, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 1 :|: z'' = 0, b2 >= 0, z1 = b1, b1 >= 0, z2 = b2, fl >= 0, z4 = i, i >= 0, z = fl, z' = 1, z3 = b3, b3 >= 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z = 2, z1 = 0, z4 = 0, z2 = 0, z3 = 0, z'' = 1, z' = 0 busy(z, z', z'', z1, z2, z3, z4) -{ 1 }-> 0 :|: z1 = 0, z4 = 0, z2 = 0, z3 = 0, z = 4, z'' = 1, z' = 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(fl, d, m, b1, b2, b3, 0) :|: z1 = b1, b1 >= 0, z2 = b2, z = fl, d >= 0, z3 = b3, b3 >= 0, z' = d, b2 >= 0, z4 = 0, fl >= 0, z'' = m, m >= 0 idle(z, z', z'', z1, z2, z3, z4) -{ 1 }-> busy(fl, d, m, or(b1, i1), or(b2, i2), or(b3, i3), i) :|: i1 >= 0, z1 = b1, b1 >= 0, z2 = b2, i >= 0, z = fl, d >= 0, z3 = b3, i2 >= 0, b3 >= 0, i3 >= 0, z' = d, b2 >= 0, fl >= 0, z4 = 1 + i1 + i2 + i3 + i, z'' = m, m >= 0 or(z, z') -{ 1 }-> b :|: b >= 0, z' = b, z = 0 or(z, z') -{ 1 }-> 1 :|: b >= 0, z = 1, z' = b start(z) -{ 1 }-> busy(2, 0, 1, 0, 0, 0, i) :|: z = i, i >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (39) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Tuples: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 S tuples: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(z0, open, down, z1, z2, z3, z4) -> c4 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) OR(true, z0) -> c41 OR(false, z0) -> c42 K tuples:none Defined Rule Symbols: start_1, busy_7, idle_7, or_2 Defined Pair Symbols: START_1, BUSY_7, IDLE_7, OR_2 Compound Symbols: c_1, c1, c2, c3, c4, c5, c6, c7, c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_2, c39_2, c40_2, c41, c42 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: START(z0) -> c(BUSY(F, closed, stop, false, false, false, z0)) Removed 9 trailing nodes: BUSY(z0, open, down, z1, z2, z3, z4) -> c4 OR(false, z0) -> c42 BUSY(FS, z0, stop, z1, z2, z3, z4) -> c2 BUSY(S, closed, stop, false, false, false, empty) -> c7 BUSY(z0, open, up, z1, z2, z3, z4) -> c3 BUSY(BF, z0, stop, z1, z2, z3, z4) -> c1 OR(true, z0) -> c41 BUSY(B, closed, stop, false, false, false, empty) -> c5 BUSY(F, closed, stop, false, false, false, empty) -> c6 ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z3, z6)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z4, z7)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9), OR(z5, z8)) K tuples:none Defined Rule Symbols: start_1, busy_7, idle_7, or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_2, c39_2, c40_2 ---------------------------------------- (43) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples:none Defined Rule Symbols: start_1, busy_7, idle_7, or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: start(z0) -> busy(F, closed, stop, false, false, false, z0) busy(BF, z0, stop, z1, z2, z3, z4) -> incorrect busy(FS, z0, stop, z1, z2, z3, z4) -> incorrect busy(z0, open, up, z1, z2, z3, z4) -> incorrect busy(z0, open, down, z1, z2, z3, z4) -> incorrect busy(B, closed, stop, false, false, false, empty) -> correct busy(F, closed, stop, false, false, false, empty) -> correct busy(S, closed, stop, false, false, false, empty) -> correct busy(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> idle(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) busy(B, open, stop, false, z0, z1, z2) -> idle(B, closed, stop, false, z0, z1, z2) busy(F, open, stop, z0, false, z1, z2) -> idle(F, closed, stop, z0, false, z1, z2) busy(S, open, stop, z0, z1, false, z2) -> idle(S, closed, stop, z0, z1, false, z2) busy(B, z0, stop, true, z1, z2, z3) -> idle(B, open, stop, false, z1, z2, z3) busy(F, z0, stop, z1, true, z2, z3) -> idle(F, open, stop, z1, false, z2, z3) busy(S, z0, stop, z1, z2, true, z3) -> idle(S, open, stop, z1, z2, false, z3) busy(B, closed, down, z0, z1, z2, z3) -> idle(B, closed, stop, z0, z1, z2, z3) busy(S, closed, up, z0, z1, z2, z3) -> idle(S, closed, stop, z0, z1, z2, z3) busy(B, closed, up, true, z0, z1, z2) -> idle(B, closed, stop, true, z0, z1, z2) busy(F, closed, up, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(F, closed, down, z0, true, z1, z2) -> idle(F, closed, stop, z0, true, z1, z2) busy(S, closed, down, z0, z1, true, z2) -> idle(S, closed, stop, z0, z1, true, z2) busy(B, closed, up, false, z0, z1, z2) -> idle(BF, closed, up, false, z0, z1, z2) busy(F, closed, up, z0, false, z1, z2) -> idle(FS, closed, up, z0, false, z1, z2) busy(F, closed, down, z0, false, z1, z2) -> idle(BF, closed, down, z0, false, z1, z2) busy(S, closed, down, z0, z1, false, z2) -> idle(FS, closed, down, z0, z1, false, z2) busy(BF, closed, up, z0, z1, z2, z3) -> idle(F, closed, up, z0, z1, z2, z3) busy(BF, closed, down, z0, z1, z2, z3) -> idle(B, closed, down, z0, z1, z2, z3) busy(FS, closed, up, z0, z1, z2, z3) -> idle(S, closed, up, z0, z1, z2, z3) busy(FS, closed, down, z0, z1, z2, z3) -> idle(F, closed, down, z0, z1, z2, z3) busy(B, closed, stop, false, true, z0, z1) -> idle(B, closed, up, false, true, z0, z1) busy(B, closed, stop, false, false, true, z0) -> idle(B, closed, up, false, false, true, z0) busy(F, closed, stop, true, false, z0, z1) -> idle(F, closed, down, true, false, z0, z1) busy(F, closed, stop, false, false, true, z0) -> idle(F, closed, up, false, false, true, z0) busy(S, closed, stop, z0, true, false, z1) -> idle(S, closed, down, z0, true, false, z1) busy(S, closed, stop, true, false, false, z0) -> idle(S, closed, down, true, false, false, z0) idle(z0, z1, z2, z3, z4, z5, empty) -> busy(z0, z1, z2, z3, z4, z5, empty) idle(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> busy(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples:none Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (47) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (48) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The (relative) TRS S consists of the following rules: or(true, z0) -> true or(false, z0) -> z0 Rewrite Strategy: INNERMOST ---------------------------------------- (49) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (50) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) or(true, z0) -> true or(false, z0) -> z0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (51) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (52) 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: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) [1] BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) [1] BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) [1] BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) [1] BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) [1] BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) [1] BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) [1] BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) [1] BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) [1] BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) [1] BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) [1] BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) [1] BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) [1] BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) [1] BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) [1] BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) [1] BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) [1] BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) [1] BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) [1] BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) [1] BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) [1] BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) [1] BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) [1] BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) [1] IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] or(true, z0) -> true [0] or(false, z0) -> z0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (53) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (54) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) [1] BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) [1] BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) [1] BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) [1] BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) [1] BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) [1] BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) [1] BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) [1] BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) [1] BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) [1] BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) [1] BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) [1] BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) [1] BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) [1] BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) [1] BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) [1] BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) [1] BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) [1] BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) [1] BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) [1] BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) [1] BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) [1] BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) [1] BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) [1] IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] or(true, z0) -> true [0] or(false, z0) -> z0 [0] The TRS has the following type information: BUSY :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true -> false:true -> false:true -> newbuttons:empty -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 B :: B:F:S:BF:FS closed :: closed:open stop :: stop:down:up false :: false:true newbuttons :: false:true -> false:true -> false:true -> newbuttons:empty -> newbuttons:empty c8 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 IDLE :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true -> false:true -> false:true -> newbuttons:empty -> c37:c38:c39:c40 F :: B:F:S:BF:FS c9 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 S :: B:F:S:BF:FS c10 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 open :: closed:open c11 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c12 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c13 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 true :: false:true c14 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c15 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c16 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 down :: stop:down:up c17 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 up :: stop:down:up c18 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c19 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c20 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c21 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c22 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c23 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 BF :: B:F:S:BF:FS c24 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 FS :: B:F:S:BF:FS c25 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c26 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c27 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c28 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c29 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c30 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c31 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c32 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c33 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c34 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c35 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c36 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 empty :: newbuttons:empty c37 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c38 :: c8:c9:c10:c11:c12:c13:c14:c15: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 or :: false:true -> false:true -> false:true c39 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c40 :: c8:c9:c10:c11:c12:c13:c14:c15: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 Rewrite Strategy: INNERMOST ---------------------------------------- (55) 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: BUSY_7 IDLE_7 (c) The following functions are completely defined: or_2 Due to the following rules being added: or(v0, v1) -> null_or [0] And the following fresh constants: null_or, const, const1 ---------------------------------------- (56) 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: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) [1] BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) [1] BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) [1] BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) [1] BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) [1] BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) [1] BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) [1] BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) [1] BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) [1] BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) [1] BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) [1] BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) [1] BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) [1] BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) [1] BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) [1] BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) [1] BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) [1] BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) [1] BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) [1] BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) [1] BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) [1] BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) [1] BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) [1] BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) [1] IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] or(true, z0) -> true [0] or(false, z0) -> z0 [0] or(v0, v1) -> null_or [0] The TRS has the following type information: BUSY :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 B :: B:F:S:BF:FS closed :: closed:open stop :: stop:down:up false :: false:true:null_or newbuttons :: false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> newbuttons:empty c8 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 IDLE :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c37:c38:c39:c40 F :: B:F:S:BF:FS c9 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 S :: B:F:S:BF:FS c10 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 open :: closed:open c11 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c12 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c13 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 true :: false:true:null_or c14 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c15 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c16 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 down :: stop:down:up c17 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 up :: stop:down:up c18 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c19 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c20 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c21 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c22 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c23 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 BF :: B:F:S:BF:FS c24 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 FS :: B:F:S:BF:FS c25 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c26 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c27 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c28 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c29 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c30 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c31 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c32 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c33 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c34 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c35 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c36 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 empty :: newbuttons:empty c37 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c38 :: c8:c9:c10:c11:c12:c13:c14:c15: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 or :: false:true:null_or -> false:true:null_or -> false:true:null_or c39 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c40 :: c8:c9:c10:c11:c12:c13:c14:c15: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 null_or :: false:true:null_or const :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 const1 :: c37:c38:c39:c40 Rewrite Strategy: INNERMOST ---------------------------------------- (57) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (58) 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: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) [1] BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) [1] BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) [1] BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) [1] BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) [1] BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) [1] BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) [1] BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) [1] BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) [1] BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) [1] BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) [1] BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) [1] BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) [1] BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) [1] BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) [1] BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) [1] BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) [1] BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) [1] BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) [1] BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) [1] BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) [1] BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) [1] BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) [1] BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) [1] IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] or(true, z0) -> true [0] or(false, z0) -> z0 [0] or(v0, v1) -> null_or [0] The TRS has the following type information: BUSY :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 B :: B:F:S:BF:FS closed :: closed:open stop :: stop:down:up false :: false:true:null_or newbuttons :: false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> newbuttons:empty c8 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 IDLE :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c37:c38:c39:c40 F :: B:F:S:BF:FS c9 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 S :: B:F:S:BF:FS c10 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 open :: closed:open c11 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c12 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c13 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 true :: false:true:null_or c14 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c15 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c16 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 down :: stop:down:up c17 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 up :: stop:down:up c18 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c19 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c20 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c21 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c22 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c23 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 BF :: B:F:S:BF:FS c24 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 FS :: B:F:S:BF:FS c25 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c26 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c27 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c28 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c29 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c30 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c31 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c32 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c33 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c34 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c35 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 c36 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 empty :: newbuttons:empty c37 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c38 :: c8:c9:c10:c11:c12:c13:c14:c15: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 or :: false:true:null_or -> false:true:null_or -> false:true:null_or c39 :: c8:c9:c10:c11:c12:c13:c14:c15: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 c40 :: c8:c9:c10:c11:c12:c13:c14:c15: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 null_or :: false:true:null_or const :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36 const1 :: c37:c38:c39:c40 Rewrite Strategy: INNERMOST ---------------------------------------- (59) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: B => 0 closed => 0 stop => 1 false => 1 F => 2 S => 4 open => 1 true => 2 down => 0 up => 2 BF => 1 FS => 3 empty => 0 null_or => 0 const => 0 const1 => 0 ---------------------------------------- (60) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z1, z2, 1, z3) :|: z10 = z1, z13 = z3, z1 >= 0, z11 = z2, z0 >= 0, z12 = 2, z = 4, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z0, z1, z2, z3) :|: z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z = 4, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 2, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z0 >= 0, z12 = 2, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 1, z2) :|: z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z' = 1, z = 4, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z0, 2, 1, z1) :|: z11 = 2, z1 >= 0, z13 = z1, z12 = 1, z0 >= 0, z = 4, z'' = 1, z10 = z0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z0) :|: z11 = 1, z13 = z0, z10 = 2, z12 = 1, z0 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z0, z1, 1, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z1, 1, z2, z3) :|: z = 2, z11 = 2, z10 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z0) :|: z = 2, z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z'' = 0, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z' = 1, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z0, z1) :|: z = 2, z12 = z0, z1 >= 0, z11 = 1, z13 = z1, z10 = 2, z0 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z0, 1, z1, z2) :|: z = 2, z'' = 0, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z10 = 2, z0 >= 0, z = 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z0, z1) :|: z11 = 2, z12 = z0, z1 >= 0, z10 = 1, z13 = z1, z0 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z0) :|: z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z = 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z12 = z1, z10 = 2, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z' = 1, z = 0, z'' = 1, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z3, z4, z5, 0) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z1 >= 0, z13 = 0, z10 = z3 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0 or(z, z') -{ 0 }-> z0 :|: z = 1, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 ---------------------------------------- (61) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: or(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 or(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> z0 :|: z = 1, z0 >= 0, z' = z0 ---------------------------------------- (62) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z1, z2, 1, z3) :|: z10 = z1, z13 = z3, z1 >= 0, z11 = z2, z0 >= 0, z12 = 2, z = 4, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z0, z1, z2, z3) :|: z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z = 4, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 2, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z0 >= 0, z12 = 2, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 1, z2) :|: z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z' = 1, z = 4, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z0, 2, 1, z1) :|: z11 = 2, z1 >= 0, z13 = z1, z12 = 1, z0 >= 0, z = 4, z'' = 1, z10 = z0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z0) :|: z11 = 1, z13 = z0, z10 = 2, z12 = 1, z0 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z0, z1, 1, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z1, 1, z2, z3) :|: z = 2, z11 = 2, z10 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z0) :|: z = 2, z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z'' = 0, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z' = 1, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z0, z1) :|: z = 2, z12 = z0, z1 >= 0, z11 = 1, z13 = z1, z10 = 2, z0 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z0, 1, z1, z2) :|: z = 2, z'' = 0, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z10 = 2, z0 >= 0, z = 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z0, z1) :|: z11 = 2, z12 = z0, z1 >= 0, z10 = 1, z13 = z1, z0 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z0) :|: z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z = 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z12 = z1, z10 = 2, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z' = 1, z = 0, z'' = 1, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', z0'', z01, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', z5 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', z0'', 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', z5 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', z0'', 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', v0 >= 0, v1 >= 0, z5 = v0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 2, z01, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', z5 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 2, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', z5 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 2, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', v0 >= 0, v1 >= 0, z5 = v0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 0, z0'', z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, z5 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 0, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, z5 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z0', 0, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 1, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, v0' >= 0, v1' >= 0, z5 = v0', z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z3, z4, z5, 0) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z1 >= 0, z13 = 0, z10 = z3 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, z0'', z01, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', z5 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, z0'', 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', z5 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, z0'', 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 1, z0'' >= 0, z7 = z0'', v0 >= 0, v1 >= 0, z5 = v0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 2, z01, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', z5 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 2, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', z5 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 2, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', z4 = 2, z0'' >= 0, z7 = z0'', v0 >= 0, v1 >= 0, z5 = v0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 0, z0'', z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, z5 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 0, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, z5 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 2, 0, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, z3 = 2, z0' >= 0, z6 = z0', v0 >= 0, v1 >= 0, z4 = v0, z7 = v1, v0' >= 0, v1' >= 0, z5 = v0', z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, z0', z0'', z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 1, z0' >= 0, z7 = z0', z5 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, z0', 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 1, z0' >= 0, z7 = z0', z5 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, z0', 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 1, z0' >= 0, z7 = z0', v0' >= 0, v1' >= 0, z5 = v0', z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 2, z0'', z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 2, z0' >= 0, z7 = z0', z5 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 2, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 2, z0' >= 0, z7 = z0', z5 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 2, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, z4 = 2, z0' >= 0, z7 = z0', v0' >= 0, v1' >= 0, z5 = v0', z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 0, z0', z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, v0' >= 0, v1' >= 0, z4 = v0', z7 = v1', z5 = 1, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 0, 2, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, v0' >= 0, v1' >= 0, z4 = v0', z7 = v1', z5 = 2, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, 0, 0, 0, z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0, v0 >= 0, v1 >= 0, z3 = v0, z6 = v1, v0' >= 0, v1' >= 0, z4 = v0', z7 = v1', v0'' >= 0, v1'' >= 0, z5 = v0'', z8 = v1'' or(z, z') -{ 0 }-> z0 :|: z = 1, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 ---------------------------------------- (63) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (64) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z10, z11, 1, z13) :|: z10 >= 0, z' >= 0, z12 = 2, z = 4, z'' = 1, z11 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z10, z11, z12, z13) :|: z = 3, z11 >= 0, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, z12, z13) :|: z11 >= 0, z10 >= 0, z'' = 2, z = 4, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 2, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z12 = 2, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 1, z13) :|: z11 >= 0, z12 = 1, z10 >= 0, z' = 1, z = 4, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z10, 2, 1, z13) :|: z11 = 2, z13 >= 0, z12 = 1, z10 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z13) :|: z11 = 1, z10 = 2, z12 = 1, z13 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z10, z11, 1, z13) :|: z'' = 0, z11 >= 0, z12 = 1, z10 >= 0, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z10, 1, z12, z13) :|: z = 2, z11 = 2, z10 >= 0, z' >= 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z10, z11, z12, z13) :|: z11 >= 0, z = 1, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z13) :|: z = 2, z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z11 = 2, z12 >= 0, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z'' = 0, z11 = 2, z12 >= 0, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z' = 1, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z = 3, z11 >= 0, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z12, z13) :|: z = 2, z13 >= 0, z11 = 1, z10 = 2, z12 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z10, 1, z12, z13) :|: z = 2, z'' = 0, z12 >= 0, z11 = 1, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z11, z12, z13) :|: z11 >= 0, z10 = 2, z' >= 0, z = 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z12, z13) :|: z11 = 2, z13 >= 0, z10 = 1, z12 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z13) :|: z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z11, z12, z13) :|: z12 >= 0, z10 = 2, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z' = 1, z = 0, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z = 1, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z10, z11, z12, 0) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z' >= 0, z13 = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, z0', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 1, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 2, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', v1'' >= 0, z8 = v1'' or(z, z') -{ 0 }-> z' :|: z = 1, z' >= 0 or(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0 or(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 ---------------------------------------- (65) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID)) Found the following analysis order by SCC decomposition: { BUSY, IDLE } { or } ---------------------------------------- (66) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z10, z11, 1, z13) :|: z10 >= 0, z' >= 0, z12 = 2, z = 4, z'' = 1, z11 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z10, z11, z12, z13) :|: z = 3, z11 >= 0, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, z12, z13) :|: z11 >= 0, z10 >= 0, z'' = 2, z = 4, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 2, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z12 = 2, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 1, z13) :|: z11 >= 0, z12 = 1, z10 >= 0, z' = 1, z = 4, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z10, 2, 1, z13) :|: z11 = 2, z13 >= 0, z12 = 1, z10 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z13) :|: z11 = 1, z10 = 2, z12 = 1, z13 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z10, z11, 1, z13) :|: z'' = 0, z11 >= 0, z12 = 1, z10 >= 0, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z10, 1, z12, z13) :|: z = 2, z11 = 2, z10 >= 0, z' >= 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z10, z11, z12, z13) :|: z11 >= 0, z = 1, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z13) :|: z = 2, z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z11 = 2, z12 >= 0, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z'' = 0, z11 = 2, z12 >= 0, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z' = 1, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z = 3, z11 >= 0, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z12, z13) :|: z = 2, z13 >= 0, z11 = 1, z10 = 2, z12 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z10, 1, z12, z13) :|: z = 2, z'' = 0, z12 >= 0, z11 = 1, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z11, z12, z13) :|: z11 >= 0, z10 = 2, z' >= 0, z = 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z12, z13) :|: z11 = 2, z13 >= 0, z10 = 1, z12 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z13) :|: z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z11, z12, z13) :|: z12 >= 0, z10 = 2, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z' = 1, z = 0, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z = 1, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z10, z11, z12, 0) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z' >= 0, z13 = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, z0', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 1, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 2, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', v1'' >= 0, z8 = v1'' or(z, z') -{ 0 }-> z' :|: z = 1, z' >= 0 or(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0 or(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 Function symbols to be analyzed: {BUSY,IDLE}, {or} ---------------------------------------- (67) ResultPropagationProof (UPPER BOUND(ID)) Applied inner abstraction using the recently inferred runtime/size bounds where possible. ---------------------------------------- (68) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z10, z11, 1, z13) :|: z10 >= 0, z' >= 0, z12 = 2, z = 4, z'' = 1, z11 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z10, z11, z12, z13) :|: z = 3, z11 >= 0, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, z12, z13) :|: z11 >= 0, z10 >= 0, z'' = 2, z = 4, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 2, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z12 = 2, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 1, z13) :|: z11 >= 0, z12 = 1, z10 >= 0, z' = 1, z = 4, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z10, 2, 1, z13) :|: z11 = 2, z13 >= 0, z12 = 1, z10 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z13) :|: z11 = 1, z10 = 2, z12 = 1, z13 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z10, z11, 1, z13) :|: z'' = 0, z11 >= 0, z12 = 1, z10 >= 0, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z10, 1, z12, z13) :|: z = 2, z11 = 2, z10 >= 0, z' >= 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z10, z11, z12, z13) :|: z11 >= 0, z = 1, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z13) :|: z = 2, z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z11 = 2, z12 >= 0, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z'' = 0, z11 = 2, z12 >= 0, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z' = 1, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z = 3, z11 >= 0, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z12, z13) :|: z = 2, z13 >= 0, z11 = 1, z10 = 2, z12 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z10, 1, z12, z13) :|: z = 2, z'' = 0, z12 >= 0, z11 = 1, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z11, z12, z13) :|: z11 >= 0, z10 = 2, z' >= 0, z = 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z12, z13) :|: z11 = 2, z13 >= 0, z10 = 1, z12 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z13) :|: z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z11, z12, z13) :|: z12 >= 0, z10 = 2, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z' = 1, z = 0, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z = 1, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z10, z11, z12, 0) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z' >= 0, z13 = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, z0', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 1, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 2, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', v1'' >= 0, z8 = v1'' or(z, z') -{ 0 }-> z' :|: z = 1, z' >= 0 or(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0 or(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 Function symbols to be analyzed: {BUSY,IDLE}, {or} ---------------------------------------- (69) IntTrsBoundProof (UPPER BOUND(ID)) Computed SIZE bound using KoAT for: BUSY after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 0 Computed SIZE bound using CoFloCo for: IDLE after applying outer abstraction to obtain an ITS, resulting in: O(1) with polynomial bound: 1 ---------------------------------------- (70) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z10, z11, 1, z13) :|: z10 >= 0, z' >= 0, z12 = 2, z = 4, z'' = 1, z11 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z10, z11, z12, z13) :|: z = 3, z11 >= 0, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, z12, z13) :|: z11 >= 0, z10 >= 0, z'' = 2, z = 4, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 2, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z12 = 2, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z10, z11, 1, z13) :|: z11 >= 0, z12 = 1, z10 >= 0, z' = 1, z = 4, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z10, 2, 1, z13) :|: z11 = 2, z13 >= 0, z12 = 1, z10 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z13) :|: z11 = 1, z10 = 2, z12 = 1, z13 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z10, z11, 1, z13) :|: z'' = 0, z11 >= 0, z12 = 1, z10 >= 0, z = 4, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z10, 1, z12, z13) :|: z = 2, z11 = 2, z10 >= 0, z' >= 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z10, z11, z12, z13) :|: z11 >= 0, z = 1, z10 >= 0, z'' = 2, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z13) :|: z = 2, z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z11 = 2, z12 >= 0, z10 >= 0, z'' = 2, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 2, z12, z13) :|: z = 2, z'' = 0, z11 = 2, z12 >= 0, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z10, 1, z12, z13) :|: z = 2, z12 >= 0, z11 = 1, z10 >= 0, z' = 1, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z = 3, z11 >= 0, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z12, z13) :|: z = 2, z13 >= 0, z11 = 1, z10 = 2, z12 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z10, 1, z12, z13) :|: z = 2, z'' = 0, z12 >= 0, z11 = 1, z10 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z11, z12, z13) :|: z11 >= 0, z10 = 2, z' >= 0, z = 0, z'' = 1, z12 >= 0, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z12, z13) :|: z11 = 2, z13 >= 0, z10 = 1, z12 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z13) :|: z10 = 1, z11 = 1, z13 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z10 >= 0, z = 0, z12 >= 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z11, z12, z13) :|: z12 >= 0, z10 = 2, z11 >= 0, z'' = 2, z = 0, z13 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z11, z12, z13) :|: z12 >= 0, z10 = 1, z11 >= 0, z' = 1, z = 0, z'' = 1, z13 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z10, z11, z12, z13) :|: z'' = 0, z11 >= 0, z = 1, z10 >= 0, z12 >= 0, z13 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z0', 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 1, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', z10, z11, z12, 0) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z' >= 0, z13 = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, z0'', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 1, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, z01, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 1, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', z12 = 2, z01 >= 0, z8 = z01 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', z11 = 2, z0'' >= 0, z7 = z0'', v1 >= 0, z8 = v1 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 2, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, z10 = 2, z0' >= 0, z6 = z0', v1 >= 0, z7 = v1, v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, z0', 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 1, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, z0'', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 1, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', z12 = 2, z0'' >= 0, z8 = z0'' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 2, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, z11 = 2, z0' >= 0, z7 = z0', v1' >= 0, z8 = v1' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, z0', z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 1, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 2, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', z12 = 2, z0' >= 0, z8 = z0' IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z, z', z'', 0, 0, 0, z9) :|: z12 >= 0, z >= 0, z11 >= 0, z'' >= 0, z10 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z' >= 0, z6 >= 0, z7 >= 0, z8 >= 0, v1 >= 0, z6 = v1, v1' >= 0, z7 = v1', v1'' >= 0, z8 = v1'' or(z, z') -{ 0 }-> z' :|: z = 1, z' >= 0 or(z, z') -{ 0 }-> 2 :|: z = 2, z' >= 0 or(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 Function symbols to be analyzed: {BUSY,IDLE}, {or} Previous analysis results are: BUSY: runtime: ?, size: O(1) [0] IDLE: runtime: ?, size: O(1) [1] ---------------------------------------- (71) 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: or(v0, v1) -> null_or [0] BUSY(v0, v1, v2, v3, v4, v5, v6) -> null_BUSY [0] And the following fresh constants: null_or, null_BUSY, const ---------------------------------------- (72) 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: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) [1] BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) [1] BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) [1] BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) [1] BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) [1] BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) [1] BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) [1] BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) [1] BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) [1] BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) [1] BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) [1] BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) [1] BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) [1] BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) [1] BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) [1] BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) [1] BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) [1] BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) [1] BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) [1] BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) [1] BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) [1] BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) [1] BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) [1] BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) [1] BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) [1] BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) [1] IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) [1] or(true, z0) -> true [0] or(false, z0) -> z0 [0] or(v0, v1) -> null_or [0] BUSY(v0, v1, v2, v3, v4, v5, v6) -> null_BUSY [0] The TRS has the following type information: BUSY :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY B :: B:F:S:BF:FS closed :: closed:open stop :: stop:down:up false :: false:true:null_or newbuttons :: false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> newbuttons:empty c8 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY IDLE :: B:F:S:BF:FS -> closed:open -> stop:down:up -> false:true:null_or -> false:true:null_or -> false:true:null_or -> newbuttons:empty -> c37:c38:c39:c40 F :: B:F:S:BF:FS c9 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY S :: B:F:S:BF:FS c10 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY open :: closed:open c11 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c12 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c13 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY true :: false:true:null_or c14 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c15 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c16 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY down :: stop:down:up c17 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY up :: stop:down:up c18 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c19 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c20 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c21 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c22 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c23 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY BF :: B:F:S:BF:FS c24 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY FS :: B:F:S:BF:FS c25 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c26 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c27 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c28 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c29 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c30 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c31 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c32 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c33 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c34 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c35 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY c36 :: c37:c38:c39:c40 -> c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY empty :: newbuttons:empty c37 :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY -> c37:c38:c39:c40 c38 :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY -> c37:c38:c39:c40 or :: false:true:null_or -> false:true:null_or -> false:true:null_or c39 :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY -> c37:c38:c39:c40 c40 :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY -> c37:c38:c39:c40 null_or :: false:true:null_or null_BUSY :: c8:c9:c10:c11:c12:c13:c14:c15:c16:c17:c18:c19:c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31:c32:c33:c34:c35:c36:null_BUSY const :: c37:c38:c39:c40 Rewrite Strategy: INNERMOST ---------------------------------------- (73) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: B => 0 closed => 0 stop => 1 false => 1 F => 2 S => 4 open => 1 true => 2 down => 0 up => 2 BF => 1 FS => 3 empty => 0 null_or => 0 null_BUSY => 0 const => 0 ---------------------------------------- (74) Obligation: Complexity RNTS consisting of the following rules: BUSY(z, z', z'', z10, z11, z12, z13) -{ 0 }-> 0 :|: v0 >= 0, z10 = v3, v6 >= 0, z'' = v2, z11 = v4, z13 = v6, v1 >= 0, v5 >= 0, z = v0, z' = v1, z12 = v5, v2 >= 0, v3 >= 0, v4 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 1, 1, z1, z2, 1, z3) :|: z10 = z1, z13 = z3, z1 >= 0, z11 = z2, z0 >= 0, z12 = 2, z = 4, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 2, z0, z1, z2, z3) :|: z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z'' = 2, z = 4, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 2, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z0 >= 0, z12 = 2, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, z0, z1, 1, z2) :|: z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z' = 1, z = 4, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 4, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, z0, 2, 1, z1) :|: z11 = 2, z1 >= 0, z13 = z1, z12 = 1, z0 >= 0, z = 4, z'' = 1, z10 = z0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(4, 0, 0, 2, 1, 1, z0) :|: z11 = 1, z13 = z0, z10 = 2, z12 = 1, z0 >= 0, z = 4, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 2, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(3, 0, 0, z0, z1, 1, z2) :|: z'' = 0, z11 = z1, z13 = z2, z1 >= 0, z12 = 1, z0 >= 0, z = 4, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 1, 1, z1, 1, z2, z3) :|: z = 2, z11 = 2, z10 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, z0, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 2, 1, 1, 2, z0) :|: z = 2, z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z'' = 2, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 2, z1, z2) :|: z = 2, z'' = 0, z11 = 2, z13 = z2, z1 >= 0, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, z0, 1, z1, z2) :|: z = 2, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z' = 1, z'' = 1, z10 = z0, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z = 2, z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z = 3, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(2, 0, 0, 2, 1, z0, z1) :|: z = 2, z12 = z0, z1 >= 0, z11 = 1, z13 = z1, z10 = 2, z0 >= 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 2, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(1, 0, 0, z0, 1, z1, z2) :|: z = 2, z'' = 0, z13 = z2, z1 >= 0, z11 = 1, z12 = z1, z0 >= 0, z10 = z0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 1, 1, 1, z1, z2, z3) :|: z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z10 = 2, z0 >= 0, z = 0, z' = z0, z'' = 1, z2 >= 0, z3 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 2, z0, z1) :|: z11 = 2, z12 = z0, z1 >= 0, z10 = 1, z13 = z1, z0 >= 0, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 2, 1, 1, 2, z0) :|: z10 = 1, z11 = 1, z13 = z0, z0 >= 0, z12 = 2, z = 0, z'' = 1, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z12 = z2, z0 >= 0, z = 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 2, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z12 = z1, z10 = 2, z0 >= 0, z'' = 2, z = 0, z2 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, z0, z1, z2) :|: z11 = z0, z13 = z2, z1 >= 0, z10 = 1, z12 = z1, z0 >= 0, z' = 1, z = 0, z'' = 1, z2 >= 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 1, 1, 1, 1, 1 + z0 + z1 + z2 + z3) :|: z1 >= 0, z10 = 1, z11 = 1, z13 = 1 + z0 + z1 + z2 + z3, z12 = 1, z0 >= 0, z = 0, z'' = 1, z2 >= 0, z3 >= 0, z' = 0 BUSY(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + IDLE(0, 0, 0, z0, z1, z2, z3) :|: z'' = 0, z11 = z1, z13 = z3, z1 >= 0, z = 1, z12 = z2, z0 >= 0, z10 = z0, z2 >= 0, z3 >= 0, z' = 0 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, z3, z4, z5, 0) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z1 >= 0, z13 = 0, z10 = z3 IDLE(z, z', z'', z10, z11, z12, z13) -{ 1 }-> 1 + BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9) :|: z'' = z2, z5 >= 0, z = z0, z11 = z4, z' = z1, z0 >= 0, z4 >= 0, z12 = z5, z2 >= 0, z3 >= 0, z13 = 1 + z6 + z7 + z8 + z9, z9 >= 0, z1 >= 0, z10 = z3, z6 >= 0, z7 >= 0, z8 >= 0 or(z, z') -{ 0 }-> z0 :|: z = 1, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 2 :|: z = 2, z0 >= 0, z' = z0 or(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (75) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) We considered the (Usable) Rules: or(true, z0) -> true or(false, z0) -> z0 And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = [1] POL(BF) = [1] POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_4 + x_7 POL(F) = [1] POL(FS) = [1] POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_4 + x_7 POL(S) = [1] POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = [1] POL(empty) = 0 POL(false) = 0 POL(newbuttons(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(open) = 0 POL(or(x_1, x_2)) = x_1 + x_2 POL(stop) = [1] POL(true) = [1] POL(up) = [1] ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (77) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) We considered the (Usable) Rules: or(true, z0) -> true or(false, z0) -> z0 And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = [1] POL(BF) = [1] POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_6 + x_7 POL(F) = [1] POL(FS) = [1] POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_6 + x_7 POL(S) = [1] POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = [1] POL(empty) = 0 POL(false) = 0 POL(newbuttons(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(open) = 0 POL(or(x_1, x_2)) = x_1 + x_2 POL(stop) = [1] POL(true) = [1] POL(up) = [1] ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (79) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) We considered the (Usable) Rules: or(true, z0) -> true or(false, z0) -> z0 And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = [1] POL(BF) = [1] POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_5 + x_7 POL(F) = [1] POL(FS) = [1] POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_5 + x_7 POL(S) = [1] POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = [1] POL(empty) = 0 POL(false) = 0 POL(newbuttons(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(open) = 0 POL(or(x_1, x_2)) = x_1 + x_2 POL(stop) = [1] POL(true) = [1] POL(up) = [1] ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (81) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) We considered the (Usable) Rules: or(true, z0) -> true or(false, z0) -> z0 And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = [1] POL(BF) = [1] POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_4 + x_5 + x_6 + x_7 POL(F) = [1] POL(FS) = [1] POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_4 + x_5 + x_6 + x_7 POL(S) = [1] POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = [1] POL(empty) = 0 POL(false) = 0 POL(newbuttons(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(open) = [1] POL(or(x_1, x_2)) = x_1 + x_2 POL(stop) = [1] POL(true) = [1] POL(up) = [1] ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (83) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) We considered the (Usable) Rules:none And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = [1] POL(BF) = [1] POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_7 POL(F) = [1] POL(FS) = [1] POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + x_7 POL(S) = [1] POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = [1] POL(empty) = 0 POL(false) = [1] POL(newbuttons(x_1, x_2, x_3, x_4)) = [1] + x_1 + x_2 + x_3 + x_4 POL(open) = 0 POL(or(x_1, x_2)) = [1] + x_1 + x_2 POL(stop) = [1] POL(true) = [1] POL(up) = [1] ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (85) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (87) CdtRuleRemovalProof (UPPER BOUND(ADD(n^2))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) We considered the (Usable) Rules: or(true, z0) -> true or(false, z0) -> z0 And the Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) The order we found is given by the following interpretation: Polynomial interpretation : POL(B) = 0 POL(BF) = 0 POL(BUSY(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = [2]x_7^2 + x_6*x_7 + x_5*x_7 + x_3*x_7 + x_3*x_4 POL(F) = 0 POL(FS) = 0 POL(IDLE(x_1, x_2, x_3, x_4, x_5, x_6, x_7)) = x_2 + [2]x_7^2 + x_3*x_7 + x_3*x_4 POL(S) = 0 POL(c10(x_1)) = x_1 POL(c11(x_1)) = x_1 POL(c12(x_1)) = x_1 POL(c13(x_1)) = x_1 POL(c14(x_1)) = x_1 POL(c15(x_1)) = x_1 POL(c16(x_1)) = x_1 POL(c17(x_1)) = x_1 POL(c18(x_1)) = x_1 POL(c19(x_1)) = x_1 POL(c20(x_1)) = x_1 POL(c21(x_1)) = x_1 POL(c22(x_1)) = x_1 POL(c23(x_1)) = x_1 POL(c24(x_1)) = x_1 POL(c25(x_1)) = x_1 POL(c26(x_1)) = x_1 POL(c27(x_1)) = x_1 POL(c28(x_1)) = x_1 POL(c29(x_1)) = x_1 POL(c30(x_1)) = x_1 POL(c31(x_1)) = x_1 POL(c32(x_1)) = x_1 POL(c33(x_1)) = x_1 POL(c34(x_1)) = x_1 POL(c35(x_1)) = x_1 POL(c36(x_1)) = x_1 POL(c37(x_1)) = x_1 POL(c38(x_1)) = x_1 POL(c39(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c8(x_1)) = x_1 POL(c9(x_1)) = x_1 POL(closed) = 0 POL(down) = 0 POL(empty) = 0 POL(false) = 0 POL(newbuttons(x_1, x_2, x_3, x_4)) = [2] + x_1 + x_2 + x_3 + x_4 POL(open) = 0 POL(or(x_1, x_2)) = [2] + x_2 POL(stop) = 0 POL(true) = [2] POL(up) = [1] ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1 ---------------------------------------- (89) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, open, stop, false, z0, z1, z2) -> c11(IDLE(B, closed, stop, false, z0, z1, z2)) by BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1 ---------------------------------------- (91) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, open, stop, z0, false, z1, z2) -> c12(IDLE(F, closed, stop, z0, false, z1, z2)) by BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1 ---------------------------------------- (93) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, open, stop, z0, z1, false, z2) -> c13(IDLE(S, closed, stop, z0, z1, false, z2)) by BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1 ---------------------------------------- (95) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, z0, stop, true, z1, z2, z3) -> c14(IDLE(B, open, stop, false, z1, z2, z3)) by BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1 ---------------------------------------- (97) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, z0, stop, z1, true, z2, z3) -> c15(IDLE(F, open, stop, z1, false, z2, z3)) by BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1 ---------------------------------------- (99) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, z0, stop, z1, z2, true, z3) -> c16(IDLE(S, open, stop, z1, z2, false, z3)) by BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1 ---------------------------------------- (101) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, down, z0, z1, z2, z3) -> c17(IDLE(B, closed, stop, z0, z1, z2, z3)) by BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1 ---------------------------------------- (103) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1 ---------------------------------------- (105) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, up, z0, z1, z2, z3) -> c18(IDLE(S, closed, stop, z0, z1, z2, z3)) by BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1 ---------------------------------------- (107) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1 ---------------------------------------- (109) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, up, true, z0, z1, z2) -> c19(IDLE(B, closed, stop, true, z0, z1, z2)) by BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1 ---------------------------------------- (111) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, up, z0, true, z1, z2) -> c20(IDLE(F, closed, stop, z0, true, z1, z2)) by BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1 ---------------------------------------- (113) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1 ---------------------------------------- (115) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, down, z0, true, z1, z2) -> c21(IDLE(F, closed, stop, z0, true, z1, z2)) by BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1 ---------------------------------------- (117) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1 ---------------------------------------- (119) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, down, z0, z1, true, z2) -> c22(IDLE(S, closed, stop, z0, z1, true, z2)) by BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1 ---------------------------------------- (121) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1 ---------------------------------------- (123) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, up, false, z0, z1, z2) -> c23(IDLE(BF, closed, up, false, z0, z1, z2)) by BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1 ---------------------------------------- (125) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1 ---------------------------------------- (127) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, up, z0, false, z1, z2) -> c24(IDLE(FS, closed, up, z0, false, z1, z2)) by BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1 ---------------------------------------- (129) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1 ---------------------------------------- (131) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, down, z0, false, z1, z2) -> c25(IDLE(BF, closed, down, z0, false, z1, z2)) by BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1 ---------------------------------------- (133) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1 ---------------------------------------- (135) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, down, z0, z1, false, z2) -> c26(IDLE(FS, closed, down, z0, z1, false, z2)) by BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1 ---------------------------------------- (137) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1 ---------------------------------------- (139) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(BF, closed, up, z0, z1, z2, z3) -> c27(IDLE(F, closed, up, z0, z1, z2, z3)) by BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1 ---------------------------------------- (141) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1 ---------------------------------------- (143) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(BF, closed, down, z0, z1, z2, z3) -> c28(IDLE(B, closed, down, z0, z1, z2, z3)) by BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1 ---------------------------------------- (145) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1 ---------------------------------------- (147) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(FS, closed, up, z0, z1, z2, z3) -> c29(IDLE(S, closed, up, z0, z1, z2, z3)) by BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1 ---------------------------------------- (149) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1 ---------------------------------------- (151) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(FS, closed, down, z0, z1, z2, z3) -> c30(IDLE(F, closed, down, z0, z1, z2, z3)) by BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1 ---------------------------------------- (153) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1 ---------------------------------------- (155) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, stop, false, true, z0, z1) -> c31(IDLE(B, closed, up, false, true, z0, z1)) by BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1 ---------------------------------------- (157) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1 ---------------------------------------- (159) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, stop, false, false, true, z0) -> c32(IDLE(B, closed, up, false, false, true, z0)) by BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1 ---------------------------------------- (161) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c33_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1 ---------------------------------------- (163) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, stop, true, false, z0, z1) -> c33(IDLE(F, closed, down, true, false, z0, z1)) by BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1 ---------------------------------------- (165) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c34_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1 ---------------------------------------- (167) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, closed, stop, false, false, true, z0) -> c34(IDLE(F, closed, up, false, false, true, z0)) by BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1 ---------------------------------------- (169) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c35_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1 ---------------------------------------- (171) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, stop, z0, true, false, z1) -> c35(IDLE(S, closed, down, z0, true, false, z1)) by BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (173) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) S tuples: BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c36_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (175) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, stop, true, false, false, z0) -> c36(IDLE(S, closed, down, true, false, false, z0)) by BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) S tuples: IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1 ---------------------------------------- (177) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) S tuples: IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c37_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1 ---------------------------------------- (179) CdtInstantiationProof (BOTH BOUNDS(ID, ID)) Use instantiation to replace IDLE(z0, z1, z2, z3, z4, z5, empty) -> c37(BUSY(z0, z1, z2, z3, z4, z5, empty)) by IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (181) CdtKnowledgeProof (BOTH BOUNDS(ID, ID)) The following tuples could be moved from S to K by knowledge propagation: BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (183) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(B, closed, stop, false, x0, x1, empty) -> c37(BUSY(B, closed, stop, false, x0, x1, empty)) by IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (185) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(F, closed, stop, x0, false, x1, empty) -> c37(BUSY(F, closed, stop, x0, false, x1, empty)) by IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (187) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, open, stop, z0, false, z1, empty) -> c12(IDLE(F, closed, stop, z0, false, z1, empty)) by BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (189) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(S, closed, stop, x0, x1, false, empty) -> c37(BUSY(S, closed, stop, x0, x1, false, empty)) by IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (191) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(F, open, stop, x1, false, x2, empty) -> c37(BUSY(F, open, stop, x1, false, x2, empty)) by IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (193) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(F, z0, stop, z1, true, z2, empty) -> c15(IDLE(F, open, stop, z1, false, z2, empty)) by BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (195) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(B, closed, stop, x0, x1, x2, empty) -> c37(BUSY(B, closed, stop, x0, x1, x2, empty)) by IDLE(B, closed, stop, true, z1, z2, empty) -> c37(BUSY(B, closed, stop, true, z1, z2, empty)) IDLE(B, closed, stop, false, true, z2, empty) -> c37(BUSY(B, closed, stop, false, true, z2, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (197) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, open, stop, false, z0, z1, empty) -> c11(IDLE(B, closed, stop, false, z0, z1, empty)) by BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) S tuples: BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (199) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, closed, down, z0, z1, z2, empty) -> c17(IDLE(B, closed, stop, z0, z1, z2, empty)) by BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) S tuples: BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (201) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(B, open, stop, false, x1, x2, empty) -> c37(BUSY(B, open, stop, false, x1, x2, empty)) by IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) S tuples: BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (203) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(B, z0, stop, true, z1, z2, empty) -> c14(IDLE(B, open, stop, false, z1, z2, empty)) by BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) S tuples: BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (205) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(S, closed, stop, x0, x1, x2, empty) -> c37(BUSY(S, closed, stop, x0, x1, x2, empty)) by IDLE(S, closed, stop, z0, z1, true, empty) -> c37(BUSY(S, closed, stop, z0, z1, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) S tuples: BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (207) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, open, stop, z0, z1, false, empty) -> c13(IDLE(S, closed, stop, z0, z1, false, empty)) by BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) S tuples: BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (209) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, closed, up, z0, z1, z2, empty) -> c18(IDLE(S, closed, stop, z0, z1, z2, empty)) by BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) S tuples: BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (211) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(S, open, stop, x1, x2, false, empty) -> c37(BUSY(S, open, stop, x1, x2, false, empty)) by IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) S tuples: BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (213) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace BUSY(S, z0, stop, z1, z2, true, empty) -> c16(IDLE(S, open, stop, z1, z2, false, empty)) by BUSY(S, z0, stop, z1, true, true, empty) -> c16(IDLE(S, open, stop, z1, true, false, empty)) BUSY(S, z0, stop, true, false, true, empty) -> c16(IDLE(S, open, stop, true, false, false, empty)) ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) BUSY(S, z0, stop, z1, true, true, empty) -> c16(IDLE(S, open, stop, z1, true, false, empty)) BUSY(S, z0, stop, true, false, true, empty) -> c16(IDLE(S, open, stop, true, false, false, empty)) S tuples: BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) BUSY(S, z0, stop, z1, true, true, empty) -> c16(IDLE(S, open, stop, z1, true, false, empty)) BUSY(S, z0, stop, true, false, true, empty) -> c16(IDLE(S, open, stop, true, false, false, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1 ---------------------------------------- (215) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) by IDLE(B, closed, stop, true, true, z1, empty) -> c37(BUSY(B, closed, stop, true, true, z1, empty)) IDLE(B, closed, stop, true, false, true, empty) -> c37(BUSY(B, closed, stop, true, false, true, empty)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: or(true, z0) -> true or(false, z0) -> z0 Tuples: BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) IDLE(B, closed, stop, true, x0, x1, empty) -> c37(BUSY(B, closed, stop, true, x0, x1, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) BUSY(S, z0, stop, z1, true, true, empty) -> c16(IDLE(S, open, stop, z1, true, false, empty)) BUSY(S, z0, stop, true, false, true, empty) -> c16(IDLE(S, open, stop, true, false, false, empty)) IDLE(B, closed, stop, true, true, z1, empty) -> c37(BUSY(B, closed, stop, true, true, z1, empty)) IDLE(B, closed, stop, true, false, true, empty) -> c37(BUSY(B, closed, stop, true, false, true, empty)) S tuples: BUSY(F, closed, up, z0, true, z1, empty) -> c20(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(F, closed, down, z0, true, z1, empty) -> c21(IDLE(F, closed, stop, z0, true, z1, empty)) BUSY(B, closed, up, false, z0, z1, empty) -> c23(IDLE(BF, closed, up, false, z0, z1, empty)) BUSY(F, closed, up, z0, false, z1, empty) -> c24(IDLE(FS, closed, up, z0, false, z1, empty)) BUSY(F, closed, down, z0, false, z1, empty) -> c25(IDLE(BF, closed, down, z0, false, z1, empty)) BUSY(S, closed, down, z0, z1, false, empty) -> c26(IDLE(FS, closed, down, z0, z1, false, empty)) BUSY(BF, closed, up, z0, z1, z2, empty) -> c27(IDLE(F, closed, up, z0, z1, z2, empty)) BUSY(BF, closed, down, z0, z1, z2, empty) -> c28(IDLE(B, closed, down, z0, z1, z2, empty)) BUSY(FS, closed, up, z0, z1, z2, empty) -> c29(IDLE(S, closed, up, z0, z1, z2, empty)) BUSY(FS, closed, down, z0, z1, z2, empty) -> c30(IDLE(F, closed, down, z0, z1, z2, empty)) BUSY(B, closed, stop, false, true, z0, empty) -> c31(IDLE(B, closed, up, false, true, z0, empty)) BUSY(B, closed, stop, false, false, true, empty) -> c32(IDLE(B, closed, up, false, false, true, empty)) BUSY(S, closed, stop, z0, true, false, empty) -> c35(IDLE(S, closed, down, z0, true, false, empty)) BUSY(S, closed, stop, true, false, false, empty) -> c36(IDLE(S, closed, down, true, false, false, empty)) IDLE(F, closed, stop, x0, true, x1, empty) -> c37(BUSY(F, closed, stop, x0, true, x1, empty)) IDLE(S, closed, stop, x0, x1, true, empty) -> c37(BUSY(S, closed, stop, x0, x1, true, empty)) IDLE(BF, closed, up, false, x0, x1, empty) -> c37(BUSY(BF, closed, up, false, x0, x1, empty)) IDLE(FS, closed, up, x0, false, x1, empty) -> c37(BUSY(FS, closed, up, x0, false, x1, empty)) IDLE(BF, closed, down, x0, false, x1, empty) -> c37(BUSY(BF, closed, down, x0, false, x1, empty)) IDLE(FS, closed, down, x0, x1, false, empty) -> c37(BUSY(FS, closed, down, x0, x1, false, empty)) IDLE(F, closed, up, x0, x1, x2, empty) -> c37(BUSY(F, closed, up, x0, x1, x2, empty)) IDLE(B, closed, down, x0, x1, x2, empty) -> c37(BUSY(B, closed, down, x0, x1, x2, empty)) IDLE(S, closed, up, x0, x1, x2, empty) -> c37(BUSY(S, closed, up, x0, x1, x2, empty)) IDLE(F, closed, down, x0, x1, x2, empty) -> c37(BUSY(F, closed, down, x0, x1, x2, empty)) IDLE(B, closed, up, false, true, x0, empty) -> c37(BUSY(B, closed, up, false, true, x0, empty)) IDLE(B, closed, up, false, false, true, empty) -> c37(BUSY(B, closed, up, false, false, true, empty)) IDLE(F, closed, down, true, false, x0, empty) -> c37(BUSY(F, closed, down, true, false, x0, empty)) IDLE(F, closed, up, false, false, true, empty) -> c37(BUSY(F, closed, up, false, false, true, empty)) IDLE(S, closed, down, x0, true, false, empty) -> c37(BUSY(S, closed, down, x0, true, false, empty)) IDLE(S, closed, down, true, false, false, empty) -> c37(BUSY(S, closed, down, true, false, false, empty)) IDLE(B, closed, stop, false, true, z1, empty) -> c37(BUSY(B, closed, stop, false, true, z1, empty)) IDLE(B, closed, stop, false, false, true, empty) -> c37(BUSY(B, closed, stop, false, false, true, empty)) IDLE(S, closed, stop, z0, true, false, empty) -> c37(BUSY(S, closed, stop, z0, true, false, empty)) IDLE(S, closed, stop, true, false, false, empty) -> c37(BUSY(S, closed, stop, true, false, false, empty)) BUSY(B, closed, down, true, z1, z2, empty) -> c17(IDLE(B, closed, stop, true, z1, z2, empty)) BUSY(B, closed, down, false, true, z2, empty) -> c17(IDLE(B, closed, stop, false, true, z2, empty)) BUSY(B, closed, down, false, false, true, empty) -> c17(IDLE(B, closed, stop, false, false, true, empty)) BUSY(S, closed, up, z0, z1, true, empty) -> c18(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(S, closed, up, z0, true, false, empty) -> c18(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, closed, up, true, false, false, empty) -> c18(IDLE(S, closed, stop, true, false, false, empty)) IDLE(B, closed, stop, true, true, z1, empty) -> c37(BUSY(B, closed, stop, true, true, z1, empty)) IDLE(B, closed, stop, true, false, true, empty) -> c37(BUSY(B, closed, stop, true, false, true, empty)) K tuples: IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c38(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c39(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) IDLE(z0, z1, z2, z3, z4, z5, newbuttons(z6, z7, z8, z9)) -> c40(BUSY(z0, z1, z2, or(z3, z6), or(z4, z7), or(z5, z8), z9)) BUSY(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c8(IDLE(B, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c9(IDLE(F, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3)) -> c10(IDLE(S, closed, stop, false, false, false, newbuttons(z0, z1, z2, z3))) BUSY(B, open, stop, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c11(IDLE(B, closed, stop, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, open, stop, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c12(IDLE(F, closed, stop, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, open, stop, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c13(IDLE(S, closed, stop, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(B, z0, stop, true, z1, z2, newbuttons(y6, y7, y8, y9)) -> c14(IDLE(B, open, stop, false, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(F, z0, stop, z1, true, z2, newbuttons(y6, y7, y8, y9)) -> c15(IDLE(F, open, stop, z1, false, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, z0, stop, z1, z2, true, newbuttons(y6, y7, y8, y9)) -> c16(IDLE(S, open, stop, z1, z2, false, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c17(IDLE(B, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c18(IDLE(S, closed, stop, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, true, z0, z1, empty) -> c19(IDLE(B, closed, stop, true, z0, z1, empty)) BUSY(B, closed, up, true, z0, z1, newbuttons(y6, y7, y8, y9)) -> c19(IDLE(B, closed, stop, true, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c20(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, true, z1, newbuttons(y6, y7, y8, y9)) -> c21(IDLE(F, closed, stop, z0, true, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, newbuttons(y6, y7, y8, y9)) -> c22(IDLE(S, closed, stop, z0, z1, true, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9)) -> c23(IDLE(BF, closed, up, false, z0, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c24(IDLE(FS, closed, up, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9)) -> c25(IDLE(BF, closed, down, z0, false, z1, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9)) -> c26(IDLE(FS, closed, down, z0, z1, false, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c27(IDLE(F, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(BF, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c28(IDLE(B, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c29(IDLE(S, closed, up, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(FS, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9)) -> c30(IDLE(F, closed, down, z0, z1, z2, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, true, z0, newbuttons(y6, y7, y8, y9)) -> c31(IDLE(B, closed, up, false, true, z0, newbuttons(y6, y7, y8, y9))) BUSY(B, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c32(IDLE(B, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, true, false, z0, newbuttons(y6, y7, y8, y9)) -> c33(IDLE(F, closed, down, true, false, z0, newbuttons(y6, y7, y8, y9))) BUSY(F, closed, stop, false, false, true, newbuttons(y6, y7, y8, y9)) -> c34(IDLE(F, closed, up, false, false, true, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, z0, true, false, newbuttons(y6, y7, y8, y9)) -> c35(IDLE(S, closed, down, z0, true, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, stop, true, false, false, newbuttons(y6, y7, y8, y9)) -> c36(IDLE(S, closed, down, true, false, false, newbuttons(y6, y7, y8, y9))) BUSY(S, closed, down, z0, z1, true, empty) -> c22(IDLE(S, closed, stop, z0, z1, true, empty)) BUSY(F, closed, stop, true, false, z0, empty) -> c33(IDLE(F, closed, down, true, false, z0, empty)) BUSY(F, closed, stop, false, false, true, empty) -> c34(IDLE(F, closed, up, false, false, true, empty)) IDLE(F, closed, stop, true, false, z1, empty) -> c37(BUSY(F, closed, stop, true, false, z1, empty)) IDLE(F, closed, stop, false, false, true, empty) -> c37(BUSY(F, closed, stop, false, false, true, empty)) BUSY(F, open, stop, true, false, z1, empty) -> c12(IDLE(F, closed, stop, true, false, z1, empty)) BUSY(F, open, stop, false, false, true, empty) -> c12(IDLE(F, closed, stop, false, false, true, empty)) IDLE(F, open, stop, true, false, z1, empty) -> c37(BUSY(F, open, stop, true, false, z1, empty)) IDLE(F, open, stop, false, false, true, empty) -> c37(BUSY(F, open, stop, false, false, true, empty)) BUSY(F, z0, stop, true, true, z2, empty) -> c15(IDLE(F, open, stop, true, false, z2, empty)) BUSY(F, z0, stop, false, true, true, empty) -> c15(IDLE(F, open, stop, false, false, true, empty)) BUSY(B, open, stop, false, true, z1, empty) -> c11(IDLE(B, closed, stop, false, true, z1, empty)) BUSY(B, open, stop, false, false, true, empty) -> c11(IDLE(B, closed, stop, false, false, true, empty)) IDLE(B, open, stop, false, true, z1, empty) -> c37(BUSY(B, open, stop, false, true, z1, empty)) IDLE(B, open, stop, false, false, true, empty) -> c37(BUSY(B, open, stop, false, false, true, empty)) BUSY(B, z0, stop, true, true, z2, empty) -> c14(IDLE(B, open, stop, false, true, z2, empty)) BUSY(B, z0, stop, true, false, true, empty) -> c14(IDLE(B, open, stop, false, false, true, empty)) BUSY(S, open, stop, z0, true, false, empty) -> c13(IDLE(S, closed, stop, z0, true, false, empty)) BUSY(S, open, stop, true, false, false, empty) -> c13(IDLE(S, closed, stop, true, false, false, empty)) IDLE(S, open, stop, z0, true, false, empty) -> c37(BUSY(S, open, stop, z0, true, false, empty)) IDLE(S, open, stop, true, false, false, empty) -> c37(BUSY(S, open, stop, true, false, false, empty)) BUSY(S, z0, stop, z1, true, true, empty) -> c16(IDLE(S, open, stop, z1, true, false, empty)) BUSY(S, z0, stop, true, false, true, empty) -> c16(IDLE(S, open, stop, true, false, false, empty)) Defined Rule Symbols: or_2 Defined Pair Symbols: BUSY_7, IDLE_7 Compound Symbols: c8_1, c9_1, c10_1, c38_1, c39_1, c40_1, c11_1, c12_1, c13_1, c14_1, c15_1, c16_1, c17_1, c18_1, c19_1, c20_1, c21_1, c22_1, c23_1, c24_1, c25_1, c26_1, c27_1, c28_1, c29_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1, c36_1, c37_1