/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 700 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 718 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval0(A, B, C, D) -> Com_1(eval1(B, B, 1, D)) :|: TRUE eval1(A, B, C, D) -> Com_1(end(A, B, C, D)) :|: A >= 101 eval1(A, B, C, D) -> Com_1(eval3(A, B, C, D)) :|: 100 >= A eval3(A, B, C, D) -> Com_1(eval3(A + 11, B, C + 1, D)) :|: 100 >= A eval3(A, B, C, D) -> Com_1(eval5(A, B, C, D)) :|: A >= 101 eval5(A, B, C, D) -> Com_1(eval7(A - 10, B, C - 1, D)) :|: C >= 2 eval7(A, B, C, D) -> Com_1(eval5(A, B, C, A - 10)) :|: A >= 101 && C >= 1 && C <= 1 eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 100 >= A eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: 2 >= C eval7(A, B, C, D) -> Com_1(eval9(A, B, C, D)) :|: C >= 0 eval9(A, B, C, D) -> Com_1(eval11(A - 10, B, C - 1, D)) :|: A >= 101 eval9(A, B, C, D) -> Com_1(eval11(A, B, C, D)) :|: 100 >= A eval11(A, B, C, D) -> Com_1(eval5(A + 11, B, C + 1, D)) :|: TRUE The start-symbols are:[eval0_4] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 258*Ar_1 + 25996) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) eval0(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval1(Ar_1, Ar_1, 1, Ar_3)) (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(end(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval3(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0, Ar_1, Ar_2, Ar_0 - 10)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval9(Ar_0, Ar_1, Ar_2, Ar_3)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1, Ar_3)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval11(Ar_0, Ar_1, Ar_2, Ar_3)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1, Ar_3)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(eval0(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [Ar_0, Ar_1, Ar_2]. We thus obtain the following problem: 2: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 2 produces the following problem: 3: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 1 Pol(eval0) = 1 Pol(eval11) = 0 Pol(eval5) = 0 Pol(eval9) = 0 Pol(eval7) = 0 Pol(eval3) = 1 Pol(eval1) = 1 Pol(end) = 0 orients all transitions weakly and the transition eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] strictly and produces the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval3) = -V_1 + 101 and size complexities S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = 1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-2) = ? S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] weakly and the transition eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval9) = 10*V_3 Pol(eval11) = 10*V_3 Pol(eval7) = 10*V_3 Pol(eval5) = 10*V_3 - 10 and size complexities S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = 1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ]", 0-2) = Ar_1 + 102 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-0) = Ar_1 + 111 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ]", 0-2) = Ar_1 + 102 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ]", 0-2) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1))", 0-2) = ? S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 orients the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) weakly and the transition eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] strictly and produces the following problem: 6: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 >= 2 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 6 to obtain the following invariants: For symbol eval1: -X_3 + 1 >= 0 /\ X_3 - 1 >= 0 /\ X_1 - X_2 >= 0 /\ -X_1 + X_2 >= 0 For symbol eval11: X_3 >= 0 /\ -X_2 + X_3 + 100 >= 0 /\ X_1 + X_3 - 91 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval3: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 >= 0 For symbol eval5: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 102 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 - 1 >= 0 /\ X_1 - 101 >= 0 For symbol eval7: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 For symbol eval9: X_3 - 1 >= 0 /\ -X_2 + X_3 + 99 >= 0 /\ X_1 + X_3 - 92 >= 0 /\ -X_2 + 100 >= 0 /\ X_1 - X_2 + 9 >= 0 /\ X_1 - 91 >= 0 This yielded the following problem: 7: T: (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval0) = -22*V_2 + 2212 Pol(eval1) = -22*V_2 + 2212 Pol(end) = -22*V_2 Pol(eval3) = -20*V_1 - 2*V_2 + 220*V_3 + 1992 Pol(eval5) = -22*V_1 + 220*V_3 + 1992 Pol(eval7) = -22*V_1 + 220*V_3 + 1992 Pol(eval9) = -22*V_1 + 220*V_3 + 1981 Pol(eval11) = -22*V_1 + 220*V_3 + 1970 Pol(koat_start) = -22*V_2 + 2212 orients all transitions weakly and the transitions eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] strictly and produces the following problem: 8: T: (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 ] with all transitions in problem 8, the following new transition is obtained: eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] We thus obtain the following problem: 9: T: (Comp: 1, Cost: 2) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 ] with all transitions in problem 9, the following new transition is obtained: eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 /\ Ar_0 + Ar_2 - 102 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] We thus obtain the following problem: 10: T: (Comp: 1, Cost: 2) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 /\ Ar_0 + Ar_2 - 102 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 1, Cost: 2) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 By chaining the transition eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] with all transitions in problem 10, the following new transition is obtained: eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] We thus obtain the following problem: 11: T: (Comp: 22*Ar_1 + 2212, Cost: 2) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 2) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 /\ Ar_0 + Ar_2 - 102 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 1, Cost: 2) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: ?, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(eval5) = V_3 - 1 Pol(eval7) = V_3 Pol(eval9) = V_3 Pol(eval11) = V_3 and size complexities S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-0) = Ar_0 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-1) = Ar_1 S("koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ]", 0-2) = Ar_2 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-0) = ? S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-1) = Ar_1 S("eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\\ -Ar_1 + Ar_2 + 100 >= 0 /\\ Ar_0 + Ar_2 - 91 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = 100 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-0) = ? S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_2 >= 0 ]", 0-2) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 2 >= Ar_2 ]", 0-2) = 2 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-0) = ? S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ Ar_0 >= 101 /\\ Ar_2 = 1 ]", 0-2) = 1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-0) = ? S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-2) = ? S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = Ar_1 + 222 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = Ar_1 + 103 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-0) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ Ar_0 >= 101 ]", 0-2) = 1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-0) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-1) = Ar_1 S("eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1))", 0-2) = 1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 ]", 0-0) = Ar_1 + 111 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 ]", 0-1) = Ar_1 S("eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\\ Ar_2 - 1 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ -Ar_0 + Ar_1 >= 0 /\\ 100 >= Ar_0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 ]", 0-2) = 2 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-0) = Ar_1 + 222 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-1) = Ar_1 S("eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 >= 0 /\\ Ar_0 >= 101 /\\ Ar_0 + Ar_2 - 102 >= 0 /\\ Ar_0 - Ar_1 - 1 >= 0 /\\ Ar_0 - 101 >= 0 /\\ Ar_2 >= 2 ]", 0-2) = Ar_1 + 105 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-0) = 100 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-1) = Ar_1 S("eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\\ -Ar_1 + Ar_2 + 99 >= 0 /\\ Ar_0 + Ar_2 - 92 >= 0 /\\ -Ar_1 + 100 >= 0 /\\ Ar_0 - Ar_1 + 9 >= 0 /\\ Ar_0 - 91 >= 0 /\\ 100 >= Ar_0 ]", 0-2) = ? orients the transitions eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] weakly and the transition eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] strictly and produces the following problem: 12: T: (Comp: 22*Ar_1 + 2212, Cost: 2) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 2) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 /\ Ar_0 + Ar_2 - 102 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 1, Cost: 2) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: ?, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: Ar_1 + 105, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: ?, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 12 produces the following problem: 13: T: (Comp: 22*Ar_1 + 2212, Cost: 2) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 1, Cost: 2) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= 101 /\ Ar_0 + Ar_2 - 102 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 1, Cost: 2) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ 100 >= Ar_0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 ] (Comp: 1, Cost: 1) eval0(Ar_0, Ar_1, Ar_2) -> Com_1(eval1(Ar_1, Ar_1, 1)) (Comp: 1, Cost: 1) eval1(Ar_0, Ar_1, Ar_2) -> Com_1(end(Ar_0, Ar_1, Ar_2)) [ -Ar_2 + 1 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 101 ] (Comp: Ar_1 + 101, Cost: 1) eval3(Ar_0, Ar_1, Ar_2) -> Com_1(eval3(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ 100 >= Ar_0 ] (Comp: 45*Ar_1 + 4529, Cost: 1) eval5(Ar_0, Ar_1, Ar_2) -> Com_1(eval7(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 102 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 - 1 >= 0 /\ Ar_0 - 101 >= 0 /\ Ar_2 >= 2 ] (Comp: 10*Ar_1 + 1030, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 /\ Ar_2 = 1 ] (Comp: 45*Ar_1 + 4530, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 2 >= Ar_2 ] (Comp: 45*Ar_1 + 4530, Cost: 1) eval7(Ar_0, Ar_1, Ar_2) -> Com_1(eval9(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_2 >= 0 ] (Comp: Ar_1 + 105, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0 - 10, Ar_1, Ar_2 - 1)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ Ar_0 >= 101 ] (Comp: 22*Ar_1 + 2212, Cost: 1) eval9(Ar_0, Ar_1, Ar_2) -> Com_1(eval11(Ar_0, Ar_1, Ar_2)) [ Ar_2 - 1 >= 0 /\ -Ar_1 + Ar_2 + 99 >= 0 /\ Ar_0 + Ar_2 - 92 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 /\ 100 >= Ar_0 ] (Comp: 45*Ar_1 + 4529, Cost: 1) eval11(Ar_0, Ar_1, Ar_2) -> Com_1(eval5(Ar_0 + 11, Ar_1, Ar_2 + 1)) [ Ar_2 >= 0 /\ -Ar_1 + Ar_2 + 100 >= 0 /\ Ar_0 + Ar_2 - 91 >= 0 /\ -Ar_1 + 100 >= 0 /\ Ar_0 - Ar_1 + 9 >= 0 /\ Ar_0 - 91 >= 0 ] (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2) -> Com_1(eval0(Ar_0, Ar_1, Ar_2)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Complexity upper bound 258*Ar_1 + 25996 Time: 0.789 sec (SMT: 0.648 sec) ---------------------------------------- (2) BOUNDS(1, n^1) ---------------------------------------- (3) Loat Proof (FINISHED) ### Pre-processing the ITS problem ### Initial linear ITS problem Start location: eval0 0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1 1: eval1 -> end : [ A>=101 ], cost: 1 2: eval1 -> eval3 : [ 100>=A ], cost: 1 3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1 4: eval3 -> eval5 : [ A>=101 ], cost: 1 5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1 6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1 7: eval7 -> eval9 : [ 100>=A ], cost: 1 8: eval7 -> eval9 : [ 2>=C ], cost: 1 9: eval7 -> eval9 : [ C>=0 ], cost: 1 10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1 11: eval9 -> eval11 : [ 100>=A ], cost: 1 12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1 Checking for constant complexity: The following rule is satisfiable with cost >= 1, yielding constant complexity: 0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1 Removed unreachable and leaf rules: Start location: eval0 0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1 2: eval1 -> eval3 : [ 100>=A ], cost: 1 3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1 4: eval3 -> eval5 : [ A>=101 ], cost: 1 5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1 6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1 7: eval7 -> eval9 : [ 100>=A ], cost: 1 8: eval7 -> eval9 : [ 2>=C ], cost: 1 9: eval7 -> eval9 : [ C>=0 ], cost: 1 10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1 11: eval9 -> eval11 : [ 100>=A ], cost: 1 12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1 ### Simplification by acceleration and chaining ### Accelerating simple loops of location 2. Accelerating the following rules: 3: eval3 -> eval3 : A'=11+A, C'=1+C, [ 100>=A ], cost: 1 Accelerated rule 3 with metering function meter (where 11*meter==100-A), yielding the new rule 13. Removing the simple loops: 3. Accelerated all simple loops using metering functions (where possible): Start location: eval0 0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1 2: eval1 -> eval3 : [ 100>=A ], cost: 1 4: eval3 -> eval5 : [ A>=101 ], cost: 1 13: eval3 -> eval3 : A'=11*meter+A, C'=meter+C, [ 100>=A && 11*meter==100-A && meter>=1 ], cost: meter 5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1 6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1 7: eval7 -> eval9 : [ 100>=A ], cost: 1 8: eval7 -> eval9 : [ 2>=C ], cost: 1 9: eval7 -> eval9 : [ C>=0 ], cost: 1 10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1 11: eval9 -> eval11 : [ 100>=A ], cost: 1 12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1 Chained accelerated rules (with incoming rules): Start location: eval0 0: eval0 -> eval1 : A'=B, C'=1, [], cost: 1 2: eval1 -> eval3 : [ 100>=A ], cost: 1 14: eval1 -> eval3 : A'=11*meter+A, C'=meter+C, [ 100>=A && 11*meter==100-A && meter>=1 ], cost: 1+meter 4: eval3 -> eval5 : [ A>=101 ], cost: 1 5: eval5 -> eval7 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 1 6: eval7 -> eval5 : D'=-10+A, [ A>=101 && C==1 ], cost: 1 7: eval7 -> eval9 : [ 100>=A ], cost: 1 8: eval7 -> eval9 : [ 2>=C ], cost: 1 9: eval7 -> eval9 : [ C>=0 ], cost: 1 10: eval9 -> eval11 : A'=-10+A, C'=-1+C, [ A>=101 ], cost: 1 11: eval9 -> eval11 : [ 100>=A ], cost: 1 12: eval11 -> eval5 : A'=11+A, C'=1+C, [], cost: 1 Eliminated locations (on tree-shaped paths): Start location: eval0 15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2 16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter 4: eval3 -> eval5 : [ A>=101 ], cost: 1 17: eval5 -> eval5 : A'=-10+A, C'=-1+C, D'=-20+A, [ -10+A>=101 && -1+C==1 ], cost: 2 18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2 19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2 20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2 21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2 22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2 Accelerating simple loops of location 3. Accelerating the following rules: 17: eval5 -> eval5 : A'=-10+A, C'=-1+C, D'=-20+A, [ -10+A>=101 && -1+C==1 ], cost: 2 Accelerated rule 17 with metering function -2+C, yielding the new rule 23. Removing the simple loops: 17. Accelerated all simple loops using metering functions (where possible): Start location: eval0 15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2 16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter 4: eval3 -> eval5 : [ A>=101 ], cost: 1 18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2 19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2 20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2 23: eval5 -> eval5 : A'=20-10*C+A, C'=2, D'=10-10*C+A, [ -10+A>=101 && -1+C==1 && -2+C>=1 ], cost: -4+2*C 21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2 22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2 Chained accelerated rules (with incoming rules): Start location: eval0 15: eval0 -> eval3 : A'=B, C'=1, [ 100>=B ], cost: 2 16: eval0 -> eval3 : A'=11*meter+B, C'=1+meter, [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter 4: eval3 -> eval5 : [ A>=101 ], cost: 1 18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2 19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2 20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2 21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2 22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2 Eliminated locations (on tree-shaped paths): Start location: eval0 24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter 18: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 100>=-10+A ], cost: 2 19: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 && 2>=-1+C ], cost: 2 20: eval5 -> eval9 : A'=-10+A, C'=-1+C, [ C>=2 ], cost: 2 21: eval9 -> eval5 : A'=1+A, C'=C, [ A>=101 ], cost: 2 22: eval9 -> eval5 : A'=11+A, C'=1+C, [ 100>=A ], cost: 2 Applied pruning (of leafs and parallel rules): Start location: eval0 24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter ### Computing asymptotic complexity ### Fully simplified ITS problem Start location: eval0 24: eval0 -> [10] : [ 100>=B && 11*meter==100-B && meter>=1 ], cost: 2+meter Computing asymptotic complexity for rule 24 Simplified the guard: 24: eval0 -> [10] : [ 11*meter==100-B && meter>=1 ], cost: 2+meter Solved the limit problem by the following transformations: Created initial limit problem: meter (+/+!), 2+meter (+), 101-11*meter-B (+/+!), -99+11*meter+B (+/+!) [not solved] removing all constraints (solved by SMT) resulting limit problem: [solved] applying transformation rule (C) using substitution {meter==n,B==100-11*n} resulting limit problem: [solved] Solution: meter / n B / 100-11*n Resulting cost 2+n has complexity: Poly(n^1) Found new complexity Poly(n^1). Obtained the following overall complexity (w.r.t. the length of the input n): Complexity: Poly(n^1) Cpx degree: 1 Solved cost: 2+n Rule cost: 2+meter Rule guard: [ 11*meter==100-B && meter>=1 ] WORST_CASE(Omega(n^1),?) ---------------------------------------- (4) BOUNDS(n^1, INF)