WORST_CASE(Omega(n^1),O(n^2))
proof of input_vWrkm5EENP.trs
# AProVE Commit ID: 5b976082cb74a395683ed8cc7acf94bd611ab29f fuhs 20230524 unpublished


The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).

(0) CpxTRS
(1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(2) CdtProblem
    (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (4) CdtProblem
    (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (6) CdtProblem
    (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) CdtProblem
    (9) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (10) CpxRelTRS
    (11) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (12) CpxWeightedTrs
    (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (14) CpxTypedWeightedTrs
    (15) CompletionProof [UPPER BOUND(ID), 0 ms]
    (16) CpxTypedWeightedCompleteTrs
    (17) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (18) CpxTypedWeightedCompleteTrs
    (19) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
    (20) CpxRNTS
    (21) InliningProof [UPPER BOUND(ID), 1659 ms]
    (22) CpxRNTS
    (23) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
    (24) CpxRNTS
    (25) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
    (26) CpxRNTS
    (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (28) CpxRNTS
    (29) IntTrsBoundProof [UPPER BOUND(ID), 130 ms]
    (30) CpxRNTS
    (31) IntTrsBoundProof [UPPER BOUND(ID), 85 ms]
    (32) CpxRNTS
    (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (34) CpxRNTS
    (35) IntTrsBoundProof [UPPER BOUND(ID), 191 ms]
    (36) CpxRNTS
    (37) IntTrsBoundProof [UPPER BOUND(ID), 5 ms]
    (38) CpxRNTS
    (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (40) CpxRNTS
    (41) IntTrsBoundProof [UPPER BOUND(ID), 148 ms]
    (42) CpxRNTS
    (43) IntTrsBoundProof [UPPER BOUND(ID), 84 ms]
    (44) CpxRNTS
    (45) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (46) CpxRNTS
    (47) IntTrsBoundProof [UPPER BOUND(ID), 321 ms]
    (48) CpxRNTS
    (49) IntTrsBoundProof [UPPER BOUND(ID), 64 ms]
    (50) CpxRNTS
    (51) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (52) CpxRNTS
    (53) IntTrsBoundProof [UPPER BOUND(ID), 149 ms]
    (54) CpxRNTS
    (55) IntTrsBoundProof [UPPER BOUND(ID), 0 ms]
    (56) CpxRNTS
    (57) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
    (58) CpxRNTS
    (59) IntTrsBoundProof [UPPER BOUND(ID), 12.2 s]
    (60) CpxRNTS
    (61) IntTrsBoundProof [UPPER BOUND(ID), 5251 ms]
    (62) CpxRNTS
    (63) FinalProof [FINISHED, 0 ms]
    (64) BOUNDS(1, n^2)
(65) CpxTrsToCdtProof [BOTH BOUNDS(ID, ID), 0 ms]
(66) CdtProblem
    (67) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (68) CpxRelTRS
    (69) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (70) CpxRelTRS
    (71) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) typed CpxTrs
    (73) OrderProof [LOWER BOUND(ID), 4 ms]
    (74) typed CpxTrs
    (75) RewriteLemmaProof [LOWER BOUND(ID), 354 ms]
    (76) typed CpxTrs
    (77) RewriteLemmaProof [LOWER BOUND(ID), 119 ms]
    (78) BEST
        (79) proven lower bound
            (80) LowerBoundPropagationProof [FINISHED, 0 ms]
            (81) BOUNDS(n^1, INF)
        (82) typed CpxTrs
            (83) RewriteLemmaProof [LOWER BOUND(ID), 112 ms]
            (84) typed CpxTrs
            (85) RewriteLemmaProof [LOWER BOUND(ID), 58 ms]
            (86) typed CpxTrs


----------------------------------------

(0)
Obligation:
The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).


The TRS R consists of the following rules:

   cond1(true, x, y) -> cond2(gr(x, 0), x, y)
   cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y)
   cond2(false, x, y) -> cond3(gr(y, 0), x, y)
   cond3(true, x, y) -> cond1(gr(add(x, y), 0), x, p(y))
   cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, y)
   gr(0, x) -> false
   gr(s(x), 0) -> true
   gr(s(x), s(y)) -> gr(x, y)
   add(0, x) -> x
   add(s(x), y) -> s(add(x, y))
   p(0) -> 0
   p(s(x)) -> x

S is empty.
Rewrite Strategy: PARALLEL_INNERMOST
----------------------------------------

(1) CpxTrsToCdtProof (UPPER BOUND(ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(2)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(0, z0) -> c7
   GR(s(z0), 0) -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0, z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0) -> c12
   P(s(z0)) -> c13
S tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(0, z0) -> c7
   GR(s(z0), 0) -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0, z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0) -> c12
   P(s(z0)) -> c13
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, cond3_3, gr_2, add_2, p_1

Defined Pair Symbols:   COND1_3, COND2_3, COND3_3, GR_2, ADD_2, P_1

Compound Symbols:   c_2, c1_3, c2_2, c3_2, c4_3, c5_2, c6_3, c7, c8, c9_1, c10, c11_1, c12, c13


----------------------------------------

(3) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 5 trailing nodes:
   P(s(z0)) -> c13
   GR(s(z0), 0) -> c8
   ADD(0, z0) -> c10
   GR(0, z0) -> c7
   P(0) -> c12

----------------------------------------

(4)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
S tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, cond3_3, gr_2, add_2, p_1

Defined Pair Symbols:   COND1_3, COND2_3, COND3_3, GR_2, ADD_2

Compound Symbols:   c_2, c1_3, c2_2, c3_2, c4_3, c5_2, c6_3, c9_1, c11_1


----------------------------------------

(5) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID))
Removed 7 trailing tuple parts
----------------------------------------

(6)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1))
S tuples:
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1))
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, cond3_3, gr_2, add_2, p_1

Defined Pair Symbols:   GR_2, ADD_2, COND1_3, COND2_3, COND3_3

Compound Symbols:   c9_1, c11_1, c_1, c1_2, c2_1, c3_1, c4_2, c5_1, c6_2


----------------------------------------

(7) CdtUsableRulesProof (BOTH BOUNDS(ID, ID))
The following rules are not usable and were removed:
   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(s(z0), s(z1)) -> gr(z0, z1)

----------------------------------------

(8)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1))
S tuples:
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1))
K tuples:none
Defined Rule Symbols:   gr_2, add_2, p_1

Defined Pair Symbols:   GR_2, ADD_2, COND1_3, COND2_3, COND3_3

Compound Symbols:   c9_1, c11_1, c_1, c1_2, c2_1, c3_1, c4_2, c5_1, c6_2


----------------------------------------

(9) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(10)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1))

The (relative) TRS S consists of the following rules:

   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(11) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(12)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c9(GR(z0, z1)) [1]
   ADD(s(z0), z1) -> c11(ADD(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1)) [1]
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1)) [1]
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1)) [1]
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1))) [1]
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   add(0, z0) -> z0 [0]
   add(s(z0), z1) -> s(add(z0, z1)) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(13) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(14)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   GR(s(z0), s(z1)) -> c9(GR(z0, z1)) [1]
   ADD(s(z0), z1) -> c11(ADD(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1)) [1]
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1)) [1]
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1)) [1]
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1))) [1]
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   add(0, z0) -> z0 [0]
   add(s(z0), z1) -> s(add(z0, z1)) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c9
s :: s:0 -> s:0
c9 :: c9 -> c9
ADD :: s:0 -> s:0 -> c11
c11 :: c11 -> c11
COND1 :: true:false -> s:0 -> s:0 -> c
true :: true:false
c :: c1:c2:c3 -> c
COND2 :: true:false -> s:0 -> s:0 -> c1:c2:c3
gr :: s:0 -> s:0 -> true:false
0 :: s:0
c1 :: c -> c11 -> c1:c2:c3
add :: s:0 -> s:0 -> s:0
p :: s:0 -> s:0
c2 :: c -> c1:c2:c3
false :: true:false
c3 :: c4:c5:c6 -> c1:c2:c3
COND3 :: true:false -> s:0 -> s:0 -> c4:c5:c6
c4 :: c -> c11 -> c4:c5:c6
c5 :: c -> c4:c5:c6
c6 :: c -> c11 -> c4:c5:c6

Rewrite Strategy: INNERMOST
----------------------------------------

(15) 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:

   GR_2
   ADD_2
   COND1_3
   COND2_3
   COND3_3

(c) The following functions are completely defined:

   gr_2
   add_2
   p_1

Due to the following rules being added:

   gr(v0, v1) -> null_gr [0]
   add(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]

And the following fresh constants:    null_gr, const, const1, const2, const3, const4

----------------------------------------

(16)
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:

   GR(s(z0), s(z1)) -> c9(GR(z0, z1)) [1]
   ADD(s(z0), z1) -> c11(ADD(z0, z1)) [1]
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1)) [1]
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), ADD(z0, z1)) [1]
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1)) [1]
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1)) [1]
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), ADD(z0, z1)) [1]
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1))) [1]
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), ADD(z0, z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   add(0, z0) -> z0 [0]
   add(s(z0), z1) -> s(add(z0, z1)) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   gr(v0, v1) -> null_gr [0]
   add(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c9
s :: s:0 -> s:0
c9 :: c9 -> c9
ADD :: s:0 -> s:0 -> c11
c11 :: c11 -> c11
COND1 :: true:false:null_gr -> s:0 -> s:0 -> c
true :: true:false:null_gr
c :: c1:c2:c3 -> c
COND2 :: true:false:null_gr -> s:0 -> s:0 -> c1:c2:c3
gr :: s:0 -> s:0 -> true:false:null_gr
0 :: s:0
c1 :: c -> c11 -> c1:c2:c3
add :: s:0 -> s:0 -> s:0
p :: s:0 -> s:0
c2 :: c -> c1:c2:c3
false :: true:false:null_gr
c3 :: c4:c5:c6 -> c1:c2:c3
COND3 :: true:false:null_gr -> s:0 -> s:0 -> c4:c5:c6
c4 :: c -> c11 -> c4:c5:c6
c5 :: c -> c4:c5:c6
c6 :: c -> c11 -> c4:c5:c6
null_gr :: true:false:null_gr
const :: c9
const1 :: c11
const2 :: c
const3 :: c1:c2:c3
const4 :: c4:c5:c6

Rewrite Strategy: INNERMOST
----------------------------------------

(17) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(18)
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:

   GR(s(z0), s(z1)) -> c9(GR(z0, z1)) [1]
   ADD(s(z0), z1) -> c11(ADD(z0, z1)) [1]
   COND1(true, 0, z1) -> c(COND2(false, 0, z1)) [1]
   COND1(true, s(z0'), z1) -> c(COND2(true, s(z0'), z1)) [1]
   COND1(true, z0, z1) -> c(COND2(null_gr, z0, z1)) [1]
   COND2(true, 0, z1) -> c1(COND1(gr(z1, 0), 0, z1), ADD(0, z1)) [1]
   COND2(true, 0, z1) -> c1(COND1(gr(z1, 0), 0, z1), ADD(0, z1)) [1]
   COND2(true, s(z0''), z1) -> c1(COND1(gr(s(add(z0'', z1)), 0), z0'', z1), ADD(s(z0''), z1)) [1]
   COND2(true, s(z0''), z1) -> c1(COND1(gr(s(add(z0'', z1)), 0), 0, z1), ADD(s(z0''), z1)) [1]
   COND2(true, 0, z1) -> c1(COND1(gr(0, 0), 0, z1), ADD(0, z1)) [1]
   COND2(true, s(z01), z1) -> c1(COND1(gr(0, 0), z01, z1), ADD(s(z01), z1)) [1]
   COND2(true, z0, z1) -> c1(COND1(gr(0, 0), 0, z1), ADD(z0, z1)) [1]
   COND2(true, 0, z1) -> c2(COND1(gr(z1, 0), 0, z1)) [1]
   COND2(true, 0, z1) -> c2(COND1(gr(z1, 0), 0, z1)) [1]
   COND2(true, s(z02), z1) -> c2(COND1(gr(s(add(z02, z1)), 0), z02, z1)) [1]
   COND2(true, s(z02), z1) -> c2(COND1(gr(s(add(z02, z1)), 0), 0, z1)) [1]
   COND2(true, 0, z1) -> c2(COND1(gr(0, 0), 0, z1)) [1]
   COND2(true, s(z03), z1) -> c2(COND1(gr(0, 0), z03, z1)) [1]
   COND2(true, z0, z1) -> c2(COND1(gr(0, 0), 0, z1)) [1]
   COND2(false, z0, 0) -> c3(COND3(false, z0, 0)) [1]
   COND2(false, z0, s(z04)) -> c3(COND3(true, z0, s(z04))) [1]
   COND2(false, z0, z1) -> c3(COND3(null_gr, z0, z1)) [1]
   COND3(true, 0, 0) -> c4(COND1(gr(0, 0), 0, 0), ADD(0, 0)) [1]
   COND3(true, 0, s(z06)) -> c4(COND1(gr(s(z06), 0), 0, z06), ADD(0, s(z06))) [1]
   COND3(true, 0, z1) -> c4(COND1(gr(z1, 0), 0, 0), ADD(0, z1)) [1]
   COND3(true, s(z05), 0) -> c4(COND1(gr(s(add(z05, 0)), 0), s(z05), 0), ADD(s(z05), 0)) [1]
   COND3(true, s(z05), s(z07)) -> c4(COND1(gr(s(add(z05, s(z07))), 0), s(z05), z07), ADD(s(z05), s(z07))) [1]
   COND3(true, s(z05), z1) -> c4(COND1(gr(s(add(z05, z1)), 0), s(z05), 0), ADD(s(z05), z1)) [1]
   COND3(true, z0, 0) -> c4(COND1(gr(0, 0), z0, 0), ADD(z0, 0)) [1]
   COND3(true, z0, s(z08)) -> c4(COND1(gr(0, 0), z0, z08), ADD(z0, s(z08))) [1]
   COND3(true, z0, z1) -> c4(COND1(gr(0, 0), z0, 0), ADD(z0, z1)) [1]
   COND3(true, 0, 0) -> c5(COND1(gr(0, 0), 0, 0)) [1]
   COND3(true, 0, s(z010)) -> c5(COND1(gr(s(z010), 0), 0, z010)) [1]
   COND3(true, 0, z1) -> c5(COND1(gr(z1, 0), 0, 0)) [1]
   COND3(true, s(z09), 0) -> c5(COND1(gr(s(add(z09, 0)), 0), s(z09), 0)) [1]
   COND3(true, s(z09), s(z011)) -> c5(COND1(gr(s(add(z09, s(z011))), 0), s(z09), z011)) [1]
   COND3(true, s(z09), z1) -> c5(COND1(gr(s(add(z09, z1)), 0), s(z09), 0)) [1]
   COND3(true, z0, 0) -> c5(COND1(gr(0, 0), z0, 0)) [1]
   COND3(true, z0, s(z012)) -> c5(COND1(gr(0, 0), z0, z012)) [1]
   COND3(true, z0, z1) -> c5(COND1(gr(0, 0), z0, 0)) [1]
   COND3(false, 0, z1) -> c6(COND1(gr(z1, 0), 0, z1), ADD(0, z1)) [1]
   COND3(false, s(z013), z1) -> c6(COND1(gr(s(add(z013, z1)), 0), s(z013), z1), ADD(s(z013), z1)) [1]
   COND3(false, z0, z1) -> c6(COND1(gr(0, 0), z0, z1), ADD(z0, z1)) [1]
   gr(0, z0) -> false [0]
   gr(s(z0), 0) -> true [0]
   add(0, z0) -> z0 [0]
   add(s(z0), z1) -> s(add(z0, z1)) [0]
   p(0) -> 0 [0]
   p(s(z0)) -> z0 [0]
   gr(v0, v1) -> null_gr [0]
   add(v0, v1) -> 0 [0]
   p(v0) -> 0 [0]

The TRS has the following type information:
GR :: s:0 -> s:0 -> c9
s :: s:0 -> s:0
c9 :: c9 -> c9
ADD :: s:0 -> s:0 -> c11
c11 :: c11 -> c11
COND1 :: true:false:null_gr -> s:0 -> s:0 -> c
true :: true:false:null_gr
c :: c1:c2:c3 -> c
COND2 :: true:false:null_gr -> s:0 -> s:0 -> c1:c2:c3
gr :: s:0 -> s:0 -> true:false:null_gr
0 :: s:0
c1 :: c -> c11 -> c1:c2:c3
add :: s:0 -> s:0 -> s:0
p :: s:0 -> s:0
c2 :: c -> c1:c2:c3
false :: true:false:null_gr
c3 :: c4:c5:c6 -> c1:c2:c3
COND3 :: true:false:null_gr -> s:0 -> s:0 -> c4:c5:c6
c4 :: c -> c11 -> c4:c5:c6
c5 :: c -> c4:c5:c6
c6 :: c -> c11 -> c4:c5:c6
null_gr :: true:false:null_gr
const :: c9
const1 :: c11
const2 :: c
const3 :: c1:c2:c3
const4 :: c4:c5:c6

Rewrite Strategy: INNERMOST
----------------------------------------

(19) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   true => 2
   0 => 0
   false => 1
   null_gr => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0

----------------------------------------

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + z0', z1) :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z0, 1 + z04) :|: z'' = 1 + z04, z04 >= 0, z = 1, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(z1, 0), 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z03, z1) :|: z = 2, z1 >= 0, z' = 1 + z03, z03 >= 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z02, z1), 0), z02, z1) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z02, z1), 0), 0, z1) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(z1, 0), 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z01, z1) + ADD(1 + z01, z1) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, z1) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z0'', z1), 0), z0'', z1) + ADD(1 + z0'', z1) :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z0'', z1), 0), 0, z1) + ADD(1 + z0'', z1) :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(z1, 0), 0, 0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, z012) :|: z = 2, z'' = 1 + z012, z0 >= 0, z012 >= 0, z' = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, 0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, 0) :|: z = 2, z'' = 0, z' = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + z010, 0), 0, z010) :|: z = 2, z'' = 1 + z010, z010 >= 0, z' = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, z1), 0), 1 + z09, 0) :|: z = 2, z1 >= 0, z' = 1 + z09, z09 >= 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, 0), 0), 1 + z09, 0) :|: z = 2, z'' = 0, z' = 1 + z09, z09 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, 1 + z011), 0), 1 + z09, z011) :|: z = 2, z011 >= 0, z' = 1 + z09, z'' = 1 + z011, z09 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(z1, 0), 0, z1) + ADD(0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(z1, 0), 0, 0) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, z08) + ADD(z0, 1 + z08) :|: z = 2, z08 >= 0, z'' = 1 + z08, z0 >= 0, z' = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, z1) + ADD(z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, 0) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), z0, 0) + ADD(z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(0, 0), 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + z06, 0), 0, z06) + ADD(0, 1 + z06) :|: z = 2, z'' = 1 + z06, z06 >= 0, z' = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z013, z1), 0), 1 + z013, z1) + ADD(1 + z013, z1) :|: z1 >= 0, z = 1, z013 >= 0, z' = 1 + z013, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, z1), 0), 1 + z05, 0) + ADD(1 + z05, z1) :|: z = 2, z1 >= 0, z05 >= 0, z' = 1 + z05, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, 0), 0), 1 + z05, 0) + ADD(1 + z05, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, 1 + z07), 0), 1 + z05, z07) + ADD(1 + z05, 1 + z07) :|: z = 2, z07 >= 0, z'' = 1 + z07, z05 >= 0, z' = 1 + z05
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   add(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0
   add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   add(z, z') -{ 0 }-> 1 + add(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(21) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0

----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + z0', z1) :|: z = 2, z1 >= 0, z0' >= 0, z' = 1 + z0', z'' = z1
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z0, 1 + z04) :|: z'' = 1 + z04, z04 >= 0, z = 1, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z02, z1), 0), z02, z1) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z02, z1), 0), 0, z1) :|: z = 2, z1 >= 0, z02 >= 0, z' = 1 + z02, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z1 = 1 + z0, z0 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z03, z1) :|: z = 2, z1 >= 0, z' = 1 + z03, z03 >= 0, z'' = z1, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, z1 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z03, z1) :|: z = 2, z1 >= 0, z' = 1 + z03, z03 >= 0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, z1 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z0'', z1), 0), z0'', z1) + ADD(1 + z0'', z1) :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z0'', z1), 0), 0, z1) + ADD(1 + z0'', z1) :|: z = 2, z1 >= 0, z' = 1 + z0'', z0'' >= 0, z'' = z1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z1 = 1 + z0, z0 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z01, z1) + ADD(1 + z01, z1) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, z1 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z01, z1) + ADD(1 + z01, z1) :|: z = 2, z1 >= 0, z01 >= 0, z' = 1 + z01, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, z1 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, z1), 0), 1 + z09, 0) :|: z = 2, z1 >= 0, z' = 1 + z09, z09 >= 0, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, 0), 0), 1 + z09, 0) :|: z = 2, z'' = 0, z' = 1 + z09, z09 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z09, 1 + z011), 0), 1 + z09, z011) :|: z = 2, z011 >= 0, z' = 1 + z09, z'' = 1 + z011, z09 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z010) :|: z = 2, z'' = 1 + z010, z010 >= 0, z' = 0, 1 + z010 = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z1 = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, z012) :|: z = 2, z'' = 1 + z012, z0 >= 0, z012 >= 0, z' = z0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, 0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, z1 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, z012) :|: z = 2, z'' = 1 + z012, z0 >= 0, z012 >= 0, z' = z0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, 0) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z010) :|: z = 2, z'' = 1 + z010, z010 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + z010 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, z1 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z013, z1), 0), 1 + z013, z1) + ADD(1 + z013, z1) :|: z1 >= 0, z = 1, z013 >= 0, z' = 1 + z013, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, z1), 0), 1 + z05, 0) + ADD(1 + z05, z1) :|: z = 2, z1 >= 0, z05 >= 0, z' = 1 + z05, z'' = z1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, 0), 0), 1 + z05, 0) + ADD(1 + z05, 0) :|: z = 2, z'' = 0, z05 >= 0, z' = 1 + z05
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z05, 1 + z07), 0), 1 + z05, z07) + ADD(1 + z05, 1 + z07) :|: z = 2, z07 >= 0, z'' = 1 + z07, z05 >= 0, z' = 1 + z05
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z06) + ADD(0, 1 + z06) :|: z = 2, z'' = 1 + z06, z06 >= 0, z' = 0, 1 + z06 = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z1) + ADD(0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1, z1 = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z1 = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, z08) + ADD(z0, 1 + z08) :|: z = 2, z08 >= 0, z'' = 1 + z08, z0 >= 0, z' = z0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, z1) + ADD(z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, 0) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z0, 0) + ADD(z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z1) + ADD(0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1, z0 >= 0, z1 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, z0 >= 0, z1 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, z08) + ADD(z0, 1 + z08) :|: z = 2, z08 >= 0, z'' = 1 + z08, z0 >= 0, z' = z0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, z1) + ADD(z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, 0) + ADD(z0, z1) :|: z = 2, z1 >= 0, z0 >= 0, z' = z0, z'' = z1, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z0, 0) + ADD(z0, 0) :|: z = 2, z'' = 0, z0 >= 0, z' = z0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z06) + ADD(0, 1 + z06) :|: z = 2, z'' = 1 + z06, z06 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + z06 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z1) + ADD(0, z1) :|: z1 >= 0, z = 1, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, z1 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z1) :|: z = 2, z1 >= 0, z' = 0, z'' = z1, v0 >= 0, v1 >= 0, z1 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z0, z1) :|: z1 >= 0, z = 1 + z0, z0 >= 0, z' = 1 + z1
   add(z, z') -{ 0 }-> z0 :|: z0 >= 0, z = 0, z' = z0
   add(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   add(z, z') -{ 0 }-> 1 + add(z0, z1) :|: z1 >= 0, z = 1 + z0, z' = z1, z0 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z = 1 + z0, z0 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z0 >= 0, z = 0, z' = z0
   gr(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   p(z) -{ 0 }-> z0 :|: z = 1 + z0, z0 >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0


----------------------------------------

(23) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0


----------------------------------------

(25) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { GR }
   { gr }
   { ADD }
   { add }
   { p }
   { COND2, COND1, COND3 }

----------------------------------------

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}

----------------------------------------

(27) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}

----------------------------------------

(29) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {GR}, {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: ?, size: O(1) [0]

----------------------------------------

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: GR
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z'

----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ 1 }-> 1 + GR(z - 1, z' - 1) :|: z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]

----------------------------------------

(33) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]

----------------------------------------

(35) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {gr}, {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: ?, size: O(1) [2]

----------------------------------------

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: gr
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(39) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]

----------------------------------------

(41) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: ADD
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {ADD}, {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: ?, size: O(1) [0]

----------------------------------------

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: ADD
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ 1 }-> 1 + ADD(z - 1, z') :|: z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + ADD(1 + (z' - 1), z'') :|: z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + ADD(1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + ADD(1 + (z' - 1), 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'') + ADD(z', z'') :|: z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) + ADD(z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) + ADD(z', 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + ADD(0, z'') :|: z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + ADD(0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + ADD(0, 1 + (z'' - 1)) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]

----------------------------------------

(45) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + s30 :|: s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + s20 :|: s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + s18 :|: s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + s19 :|: s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]

----------------------------------------

(47) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: add
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z + z'

----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + s30 :|: s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + s20 :|: s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + s18 :|: s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + s19 :|: s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {add}, {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: ?, size: O(n^1) [z + z']

----------------------------------------

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: add
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 0, z'') + s4 :|: s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), z' - 1, z'') + s3 :|: s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) :|: z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) :|: z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), z'') + s30 :|: s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, z''), 0), 1 + (z' - 1), 0) + s20 :|: s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 0), 0), 1 + (z' - 1), 0) + s18 :|: s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(gr(1 + add(z' - 1, 1 + (z'' - 1)), 0), 1 + (z' - 1), z'' - 1) + s19 :|: s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + add(z - 1, z') :|: z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(51) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']

----------------------------------------

(53) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {p}, {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: ?, size: O(n^1) [z]

----------------------------------------

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: p
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(57) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]

----------------------------------------

(59) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: COND2
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

Computed SIZE bound using CoFloCo for: COND1
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

Computed SIZE bound using CoFloCo for: COND3
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 2

----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: {COND2,COND1,COND3}
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: ?, size: O(1) [0]
  COND1: runtime: ?, size: O(1) [1]
  COND3: runtime: ?, size: O(1) [2]

----------------------------------------

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using KoAT for: COND2
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 202 + 187*z' + 29*z'*z'' + 29*z'^2 + 152*z''

Computed RUNTIME bound using KoAT for: COND1
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 609 + 374*z' + 58*z'*z'' + 58*z'^2 + 456*z''

Computed RUNTIME bound using KoAT for: COND3
after applying outer abstraction to obtain an ITS,
resulting in: O(n^2) with polynomial bound: 18620 + 7518*z' + 522*z'*z'' + 1218*z'^2 + 7296*z''

----------------------------------------

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   ADD(z, z') -{ z }-> 1 + s' :|: s' >= 0, s' <= 0, z' >= 0, z - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(2, 1 + (z' - 1), z'') :|: z = 2, z'' >= 0, z' - 1 >= 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0
   COND1(z, z', z'') -{ 1 }-> 1 + COND2(0, z', z'') :|: z = 2, z'' >= 0, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(2, z', 1 + (z'' - 1)) :|: z'' - 1 >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND3(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s39, z' - 1, z'') :|: s38 >= 0, s38 <= z' - 1 + z'', s39 >= 0, s39 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(s41, 0, z'') :|: s40 >= 0, s40 <= z' - 1 + z'', s41 >= 0, s41 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, z' - 1, z'') :|: z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s35, z' - 1, z'') + s3 :|: s34 >= 0, s34 <= z' - 1 + z'', s35 >= 0, s35 <= 2, s3 >= 0, s3 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(s37, 0, z'') + s4 :|: s36 >= 0, s36 <= z' - 1 + z'', s37 >= 0, s37 <= 2, s4 >= 0, s4 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s'' :|: s'' >= 0, s'' <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, 0, z'') + s10 :|: s10 >= 0, s10 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s2 :|: s2 >= 0, s2 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s6 :|: s6 >= 0, s6 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z' - 1, z'') + s8 :|: s8 >= 0, s8 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, z0 >= 0, 0 = 0, 0 = z0
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s1 :|: s1 >= 0, s1 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND2(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s5 :|: s5 >= 0, s5 <= 0, z = 2, z'' >= 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, 0, z'') + s9 :|: s9 >= 0, s9 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND2(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z' - 1, z'') + s7 :|: s7 >= 0, s7 <= 0, z = 2, z'' >= 0, z' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s49, 1 + (z' - 1), 0) :|: s48 >= 0, s48 <= z' - 1 + 0, s49 >= 0, s49 <= 2, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s51, 1 + (z' - 1), z'' - 1) :|: s50 >= 0, s50 <= z' - 1 + (1 + (z'' - 1)), s51 >= 0, s51 <= 2, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(s53, 1 + (z' - 1), 0) :|: s52 >= 0, s52 <= z' - 1 + z'', s53 >= 0, s53 <= 2, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', 0) :|: z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) :|: z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', 0) :|: z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, z', z'' - 1) :|: z = 2, z' >= 0, z'' - 1 >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) :|: z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) :|: z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s43, 1 + (z' - 1), 0) + s18 :|: s42 >= 0, s42 <= z' - 1 + 0, s43 >= 0, s43 <= 2, s18 >= 0, s18 <= 0, z = 2, z'' = 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s45, 1 + (z' - 1), z'' - 1) + s19 :|: s44 >= 0, s44 <= z' - 1 + (1 + (z'' - 1)), s45 >= 0, s45 <= 2, s19 >= 0, s19 <= 0, z = 2, z'' - 1 >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s47, 1 + (z' - 1), 0) + s20 :|: s46 >= 0, s46 <= z' - 1 + z'', s47 >= 0, s47 <= 2, s20 >= 0, s20 <= 0, z = 2, z'' >= 0, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(s55, 1 + (z' - 1), z'') + s30 :|: s54 >= 0, s54 <= z' - 1 + z'', s55 >= 0, s55 <= 2, s30 >= 0, s30 <= 0, z'' >= 0, z = 1, z' - 1 >= 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'') + s27 :|: s27 >= 0, s27 <= 0, z'' >= 0, z = 1, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, 0) + s15 :|: s15 >= 0, s15 <= 0, z = 2, z'' >= 0, z' = 0, z'' - 1 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(2, 0, z'' - 1) + s13 :|: s13 >= 0, s13 <= 0, z = 2, z'' - 1 >= 0, z' = 0, 1 + (z'' - 1) = 1 + z0, z0 >= 0, 0 = 0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'') + s32 :|: s32 >= 0, s32 <= 0, z'' >= 0, z = 1, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s22 :|: s22 >= 0, s22 <= 0, z = 2, z'' = 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', 0) + s26 :|: s26 >= 0, s26 <= 0, z = 2, z'' >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(1, z', z'' - 1) + s24 :|: s24 >= 0, s24 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, z0' >= 0, 0 = 0, 0 = z0'
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, z'') + s29 :|: s29 >= 0, s29 <= 0, z'' >= 0, z = 1, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s12 :|: s12 >= 0, s12 <= 0, z = 2, z'' = 0, z' = 0, z0 >= 0, 0 = 0, 0 = z0
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(1, 0, 0) + s17 :|: s17 >= 0, s17 <= 0, z = 2, z'' >= 0, z' = 0, z0 >= 0, z'' = 0, 0 = z0
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'') + s31 :|: s31 >= 0, s31 <= 0, z'' >= 0, z = 1, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s21 :|: s21 >= 0, s21 <= 0, z = 2, z'' = 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', 0) + s25 :|: s25 >= 0, s25 <= 0, z = 2, z'' >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 + z' }-> 1 + COND1(0, z', z'' - 1) + s23 :|: s23 >= 0, s23 <= 0, z = 2, z'' - 1 >= 0, z' >= 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'') + s28 :|: s28 >= 0, s28 <= 0, z'' >= 0, z = 1, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s11 :|: s11 >= 0, s11 <= 0, z = 2, z'' = 0, z' = 0, v0 >= 0, v1 >= 0, 0 = v0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, 0) + s16 :|: s16 >= 0, s16 <= 0, z = 2, z'' >= 0, z' = 0, v1 >= 0, 0 = v1
   COND3(z, z', z'') -{ 1 }-> 1 + COND1(0, 0, z'' - 1) + s14 :|: s14 >= 0, s14 <= 0, z = 2, z'' - 1 >= 0, z' = 0, v0 >= 0, v1 >= 0, 1 + (z'' - 1) = v0, 0 = v1
   GR(z, z') -{ z' }-> 1 + s :|: s >= 0, s <= 0, z' - 1 >= 0, z - 1 >= 0
   add(z, z') -{ 0 }-> z' :|: z' >= 0, z = 0
   add(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   add(z, z') -{ 0 }-> 1 + s33 :|: s33 >= 0, s33 <= z - 1 + z', z' >= 0, z - 1 >= 0
   gr(z, z') -{ 0 }-> 2 :|: z - 1 >= 0, z' = 0
   gr(z, z') -{ 0 }-> 1 :|: z' >= 0, z = 0
   gr(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   p(z) -{ 0 }-> 0 :|: z = 0
   p(z) -{ 0 }-> 0 :|: z >= 0
   p(z) -{ 0 }-> z - 1 :|: z - 1 >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  GR: runtime: O(n^1) [z'], size: O(1) [0]
  gr: runtime: O(1) [0], size: O(1) [2]
  ADD: runtime: O(n^1) [z], size: O(1) [0]
  add: runtime: O(1) [0], size: O(n^1) [z + z']
  p: runtime: O(1) [0], size: O(n^1) [z]
  COND2: runtime: O(n^2) [202 + 187*z' + 29*z'*z'' + 29*z'^2 + 152*z''], size: O(1) [0]
  COND1: runtime: O(n^2) [609 + 374*z' + 58*z'*z'' + 58*z'^2 + 456*z''], size: O(1) [1]
  COND3: runtime: O(n^2) [18620 + 7518*z' + 522*z'*z'' + 1218*z'^2 + 7296*z''], size: O(1) [2]

----------------------------------------

(63) FinalProof (FINISHED)
Computed overall runtime complexity
----------------------------------------

(64)
BOUNDS(1, n^2)

----------------------------------------

(65) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID))
Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT
----------------------------------------

(66)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0
Tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(0, z0) -> c7
   GR(s(z0), 0) -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0, z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0) -> c12
   P(s(z0)) -> c13
S tuples:
   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(0, z0) -> c7
   GR(s(z0), 0) -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0, z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0) -> c12
   P(s(z0)) -> c13
K tuples:none
Defined Rule Symbols:   cond1_3, cond2_3, cond3_3, gr_2, add_2, p_1

Defined Pair Symbols:   COND1_3, COND2_3, COND3_3, GR_2, ADD_2, P_1

Compound Symbols:   c_2, c1_3, c2_2, c3_2, c4_3, c5_2, c6_3, c7, c8, c9_1, c10, c11_1, c12, c13


----------------------------------------

(67) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID))
Converted S to standard rules, and D \ S as well as R to relative rules.
----------------------------------------

(68)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   COND1(true, z0, z1) -> c(COND2(gr(z0, 0), z0, z1), GR(z0, 0))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0), p(z0), z1), GR(add(z0, z1), 0), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0), z0, z1), GR(z1, 0))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0), z0, p(z1)), GR(add(z0, z1), 0), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0), z0, z1), GR(add(z0, z1), 0), ADD(z0, z1))
   GR(0, z0) -> c7
   GR(s(z0), 0) -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0, z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0) -> c12
   P(s(z0)) -> c13

The (relative) TRS S consists of the following rules:

   cond1(true, z0, z1) -> cond2(gr(z0, 0), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0), z0, z1)
   gr(0, z0) -> false
   gr(s(z0), 0) -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0, z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0) -> 0
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(69) RenamingProof (BOTH BOUNDS(ID, ID))
Renamed function symbols to avoid clashes with predefined symbol.
----------------------------------------

(70)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF).


The TRS R consists of the following rules:

   COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
   COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
   COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
   COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
   COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
   COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
   COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
   GR(0', z0) -> c7
   GR(s(z0), 0') -> c8
   GR(s(z0), s(z1)) -> c9(GR(z0, z1))
   ADD(0', z0) -> c10
   ADD(s(z0), z1) -> c11(ADD(z0, z1))
   P(0') -> c12
   P(s(z0)) -> c13

The (relative) TRS S consists of the following rules:

   cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
   cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
   cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
   cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
   cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
   gr(0', z0) -> false
   gr(s(z0), 0') -> true
   gr(s(z0), s(z1)) -> gr(z0, z1)
   add(0', z0) -> z0
   add(s(z0), z1) -> s(add(z0, z1))
   p(0') -> 0'
   p(s(z0)) -> z0

Rewrite Strategy: INNERMOST
----------------------------------------

(71) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Inferred types.
----------------------------------------

(72)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11

----------------------------------------

(73) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
COND1, COND2, gr, GR, add, ADD, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
gr < COND1
GR < COND1
COND1 = COND3
gr < COND2
GR < COND2
add < COND2
ADD < COND2
COND2 = COND3
gr < COND3
gr < cond1
gr < cond2
gr < cond3
GR < COND3
add < COND3
add < cond2
add < cond3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(74)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
gr, COND1, COND2, GR, add, ADD, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
gr < COND1
GR < COND1
COND1 = COND3
gr < COND2
GR < COND2
add < COND2
ADD < COND2
COND2 = COND3
gr < COND3
gr < cond1
gr < cond2
gr < cond3
GR < COND3
add < COND3
add < cond2
add < cond3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(75) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)

Induction Base:
gr(gen_0':s10_14(0), gen_0':s10_14(0)) ->_R^Omega(0)
false

Induction Step:
gr(gen_0':s10_14(+(n14_14, 1)), gen_0':s10_14(+(n14_14, 1))) ->_R^Omega(0)
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) ->_IH
false

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(76)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Lemmas:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
GR, COND1, COND2, add, ADD, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
GR < COND1
COND1 = COND3
GR < COND2
add < COND2
ADD < COND2
COND2 = COND3
GR < COND3
add < COND3
add < cond2
add < cond3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(77) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
GR(gen_0':s10_14(n389_14), gen_0':s10_14(n389_14)) -> gen_c7:c8:c911_14(n389_14), rt in Omega(1 + n389_14)

Induction Base:
GR(gen_0':s10_14(0), gen_0':s10_14(0)) ->_R^Omega(1)
c7

Induction Step:
GR(gen_0':s10_14(+(n389_14, 1)), gen_0':s10_14(+(n389_14, 1))) ->_R^Omega(1)
c9(GR(gen_0':s10_14(n389_14), gen_0':s10_14(n389_14))) ->_IH
c9(gen_c7:c8:c911_14(c390_14))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(78)
Complex Obligation (BEST)

----------------------------------------

(79)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Lemmas:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
GR, COND1, COND2, add, ADD, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
GR < COND1
COND1 = COND3
GR < COND2
add < COND2
ADD < COND2
COND2 = COND3
GR < COND3
add < COND3
add < cond2
add < cond3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(80) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(81)
BOUNDS(n^1, INF)

----------------------------------------

(82)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Lemmas:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)
GR(gen_0':s10_14(n389_14), gen_0':s10_14(n389_14)) -> gen_c7:c8:c911_14(n389_14), rt in Omega(1 + n389_14)


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
add, COND1, COND2, ADD, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
COND1 = COND3
add < COND2
ADD < COND2
COND2 = COND3
add < COND3
add < cond2
add < cond3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(83) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
add(gen_0':s10_14(n1032_14), gen_0':s10_14(b)) -> gen_0':s10_14(+(n1032_14, b)), rt in Omega(0)

Induction Base:
add(gen_0':s10_14(0), gen_0':s10_14(b)) ->_R^Omega(0)
gen_0':s10_14(b)

Induction Step:
add(gen_0':s10_14(+(n1032_14, 1)), gen_0':s10_14(b)) ->_R^Omega(0)
s(add(gen_0':s10_14(n1032_14), gen_0':s10_14(b))) ->_IH
s(gen_0':s10_14(+(b, c1033_14)))

We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0).
----------------------------------------

(84)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Lemmas:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)
GR(gen_0':s10_14(n389_14), gen_0':s10_14(n389_14)) -> gen_c7:c8:c911_14(n389_14), rt in Omega(1 + n389_14)
add(gen_0':s10_14(n1032_14), gen_0':s10_14(b)) -> gen_0':s10_14(+(n1032_14, b)), rt in Omega(0)


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
ADD, COND1, COND2, COND3, cond1, cond2, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
COND1 = COND3
ADD < COND2
COND2 = COND3
ADD < COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3

----------------------------------------

(85) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
ADD(gen_0':s10_14(n2099_14), gen_0':s10_14(b)) -> gen_c10:c1112_14(n2099_14), rt in Omega(1 + n2099_14)

Induction Base:
ADD(gen_0':s10_14(0), gen_0':s10_14(b)) ->_R^Omega(1)
c10

Induction Step:
ADD(gen_0':s10_14(+(n2099_14, 1)), gen_0':s10_14(b)) ->_R^Omega(1)
c11(ADD(gen_0':s10_14(n2099_14), gen_0':s10_14(b))) ->_IH
c11(gen_c10:c1112_14(c2100_14))

We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n).
----------------------------------------

(86)
Obligation:
Innermost TRS:
Rules:
COND1(true, z0, z1) -> c(COND2(gr(z0, 0'), z0, z1), GR(z0, 0'))
COND2(true, z0, z1) -> c1(COND1(gr(add(z0, z1), 0'), p(z0), z1), GR(add(z0, z1), 0'), ADD(z0, z1))
COND2(true, z0, z1) -> c2(COND1(gr(add(z0, z1), 0'), p(z0), z1), P(z0))
COND2(false, z0, z1) -> c3(COND3(gr(z1, 0'), z0, z1), GR(z1, 0'))
COND3(true, z0, z1) -> c4(COND1(gr(add(z0, z1), 0'), z0, p(z1)), GR(add(z0, z1), 0'), ADD(z0, z1))
COND3(true, z0, z1) -> c5(COND1(gr(add(z0, z1), 0'), z0, p(z1)), P(z1))
COND3(false, z0, z1) -> c6(COND1(gr(add(z0, z1), 0'), z0, z1), GR(add(z0, z1), 0'), ADD(z0, z1))
GR(0', z0) -> c7
GR(s(z0), 0') -> c8
GR(s(z0), s(z1)) -> c9(GR(z0, z1))
ADD(0', z0) -> c10
ADD(s(z0), z1) -> c11(ADD(z0, z1))
P(0') -> c12
P(s(z0)) -> c13
cond1(true, z0, z1) -> cond2(gr(z0, 0'), z0, z1)
cond2(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), p(z0), z1)
cond2(false, z0, z1) -> cond3(gr(z1, 0'), z0, z1)
cond3(true, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, p(z1))
cond3(false, z0, z1) -> cond1(gr(add(z0, z1), 0'), z0, z1)
gr(0', z0) -> false
gr(s(z0), 0') -> true
gr(s(z0), s(z1)) -> gr(z0, z1)
add(0', z0) -> z0
add(s(z0), z1) -> s(add(z0, z1))
p(0') -> 0'
p(s(z0)) -> z0

Types:
COND1 :: true:false -> 0':s -> 0':s -> c
true :: true:false
c :: c1:c2:c3 -> c7:c8:c9 -> c
COND2 :: true:false -> 0':s -> 0':s -> c1:c2:c3
gr :: 0':s -> 0':s -> true:false
0' :: 0':s
GR :: 0':s -> 0':s -> c7:c8:c9
c1 :: c -> c7:c8:c9 -> c10:c11 -> c1:c2:c3
add :: 0':s -> 0':s -> 0':s
p :: 0':s -> 0':s
ADD :: 0':s -> 0':s -> c10:c11
c2 :: c -> c12:c13 -> c1:c2:c3
P :: 0':s -> c12:c13
false :: true:false
c3 :: c4:c5:c6 -> c7:c8:c9 -> c1:c2:c3
COND3 :: true:false -> 0':s -> 0':s -> c4:c5:c6
c4 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c5 :: c -> c12:c13 -> c4:c5:c6
c6 :: c -> c7:c8:c9 -> c10:c11 -> c4:c5:c6
c7 :: c7:c8:c9
s :: 0':s -> 0':s
c8 :: c7:c8:c9
c9 :: c7:c8:c9 -> c7:c8:c9
c10 :: c10:c11
c11 :: c10:c11 -> c10:c11
c12 :: c12:c13
c13 :: c12:c13
cond1 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond2 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
cond3 :: true:false -> 0':s -> 0':s -> cond1:cond2:cond3
hole_c1_14 :: c
hole_true:false2_14 :: true:false
hole_0':s3_14 :: 0':s
hole_c1:c2:c34_14 :: c1:c2:c3
hole_c7:c8:c95_14 :: c7:c8:c9
hole_c10:c116_14 :: c10:c11
hole_c12:c137_14 :: c12:c13
hole_c4:c5:c68_14 :: c4:c5:c6
hole_cond1:cond2:cond39_14 :: cond1:cond2:cond3
gen_0':s10_14 :: Nat -> 0':s
gen_c7:c8:c911_14 :: Nat -> c7:c8:c9
gen_c10:c1112_14 :: Nat -> c10:c11


Lemmas:
gr(gen_0':s10_14(n14_14), gen_0':s10_14(n14_14)) -> false, rt in Omega(0)
GR(gen_0':s10_14(n389_14), gen_0':s10_14(n389_14)) -> gen_c7:c8:c911_14(n389_14), rt in Omega(1 + n389_14)
add(gen_0':s10_14(n1032_14), gen_0':s10_14(b)) -> gen_0':s10_14(+(n1032_14, b)), rt in Omega(0)
ADD(gen_0':s10_14(n2099_14), gen_0':s10_14(b)) -> gen_c10:c1112_14(n2099_14), rt in Omega(1 + n2099_14)


Generator Equations:
gen_0':s10_14(0) <=> 0'
gen_0':s10_14(+(x, 1)) <=> s(gen_0':s10_14(x))
gen_c7:c8:c911_14(0) <=> c7
gen_c7:c8:c911_14(+(x, 1)) <=> c9(gen_c7:c8:c911_14(x))
gen_c10:c1112_14(0) <=> c10
gen_c10:c1112_14(+(x, 1)) <=> c11(gen_c10:c1112_14(x))


The following defined symbols remain to be analysed:
cond2, COND1, COND2, COND3, cond1, cond3

They will be analysed ascendingly in the following order:
COND1 = COND2
COND1 = COND3
COND2 = COND3
cond1 = cond2
cond1 = cond3
cond2 = cond3