28.00/19.36 WORST_CASE(Omega(n^1), O(n^2)) 28.02/19.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 28.02/19.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.02/19.37 28.02/19.37 28.02/19.37 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2). 28.02/19.37 28.02/19.37 (0) CpxIntTrs 28.02/19.37 (1) Koat Proof [FINISHED, 820 ms] 28.02/19.37 (2) BOUNDS(1, n^2) 28.02/19.37 (3) Loat Proof [FINISHED, 5619 ms] 28.02/19.37 (4) BOUNDS(n^1, INF) 28.02/19.37 28.02/19.37 28.02/19.37 ---------------------------------------- 28.02/19.37 28.02/19.37 (0) 28.02/19.37 Obligation: 28.02/19.37 Complexity Int TRS consisting of the following rules: 28.02/19.37 f0(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, 0, B, E, F, G, H)) :|: A >= B + 1 28.02/19.37 f12(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, C, D, E + 1, J, I, H)) :|: A >= E && I >= J 28.02/19.37 f12(A, B, C, D, E, F, G, H) -> Com_1(f12(A, B, J, E, E + 1, I, K, H)) :|: A >= E && I >= 1 + K 28.02/19.37 f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E + 1, F, G, J)) :|: A >= E 28.02/19.37 f29(A, B, C, D, E, F, G, H) -> Com_1(f29(A, B, C, D, E + 1, F, G, J)) :|: A >= E 28.02/19.37 f35(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D, E, F, G, H)) :|: 0 >= C + 1 28.02/19.37 f35(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D, E, F, G, H)) :|: C >= 1 28.02/19.37 f37(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && 0 >= I + 1 28.02/19.37 f37(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, J)) :|: A >= D && I >= 1 28.02/19.37 f43(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E + 1, F, G, H)) :|: A >= E 28.02/19.37 f48(A, B, C, D, E, F, G, H) -> Com_1(f48(A, B, C, D, E + 1, F, G, H)) :|: A >= E 28.02/19.37 f37(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D + 1, E, F, G, 0)) :|: A >= D 28.02/19.37 f35(A, B, C, D, E, F, G, H) -> Com_1(f0(A, B + 1, 0, D, E, F, G, H)) :|: C >= 0 && C <= 0 28.02/19.37 f48(A, B, C, D, E, F, G, H) -> Com_1(f37(A, B, C, D + 1, E, F, G, H)) :|: E >= 1 + A 28.02/19.37 f43(A, B, C, D, E, F, G, H) -> Com_1(f48(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 28.02/19.37 f37(A, B, C, D, E, F, G, H) -> Com_1(f0(A, B + 1, C, D, E, F, G, H)) :|: D >= 1 + A 28.02/19.37 f29(A, B, C, D, E, F, G, H) -> Com_1(f35(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 28.02/19.37 f22(A, B, C, D, E, F, G, H) -> Com_1(f29(A, B, C, D, E, F, G, H)) :|: E >= 1 + A 28.02/19.37 f12(A, B, C, D, E, F, G, H) -> Com_1(f35(A, B, C, B, E, F, G, H)) :|: E >= 1 + A && B >= D && B <= D 28.02/19.37 f12(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G, H)) :|: B >= D + 1 && E >= 1 + A 28.02/19.37 f12(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G, H)) :|: D >= 1 + B && E >= 1 + A 28.02/19.37 f0(A, B, C, D, E, F, G, H) -> Com_1(f58(A, B, C, D, E, F, G, H)) :|: B >= A 28.02/19.37 start(A, B, C, D, E, F, G, H) -> Com_1(f0(A, B, C, D, E, F, G, H)) :|: TRUE 28.02/19.37 28.02/19.37 The start-symbols are:[start_8] 28.02/19.37 28.02/19.37 28.02/19.37 ---------------------------------------- 28.02/19.37 28.02/19.37 (1) Koat Proof (FINISHED) 28.02/19.37 YES(?, 312460831275774*ar_0 + 44637261614347*ar_1 + 267823569665387*ar_4 + 5040*ar_0^2 + 9150*ar_0*ar_4 + 5550*ar_0*ar_1 + 4830*ar_1*ar_4 + 690*ar_1^2 + 4140*ar_4^2 + 267823569661249) 28.02/19.37 28.02/19.37 28.02/19.37 28.02/19.37 Initial complexity problem: 28.02/19.37 28.02/19.37 1: T: 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_1 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, j, i, ar_7)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1, i, k, ar_7)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, j)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_2 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, j)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, 0)) [ ar_0 >= ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 = 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4, ar_5, ar_6, ar_7)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_1 >= ar_0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 28.02/19.37 28.02/19.37 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] 28.02/19.37 28.02/19.37 start location: koat_start 28.02/19.37 28.02/19.37 leaf cost: 0 28.02/19.37 28.02/19.37 28.02/19.37 28.02/19.37 Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4]. 28.02/19.37 28.02/19.37 We thus obtain the following problem: 28.02/19.37 28.02/19.37 2: T: 28.02/19.37 28.02/19.37 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.37 28.02/19.37 start location: koat_start 28.02/19.37 28.02/19.37 leaf cost: 0 28.02/19.37 28.02/19.37 28.02/19.37 28.02/19.37 Testing for reachability in the complexity graph removes the following transitions from problem 2: 28.02/19.37 28.02/19.37 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 We thus obtain the following problem: 28.02/19.37 28.02/19.37 3: T: 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.37 28.02/19.37 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.37 28.02/19.37 start location: koat_start 28.02/19.37 28.02/19.37 leaf cost: 0 28.02/19.37 28.02/19.37 28.02/19.37 28.02/19.37 Repeatedly propagating knowledge in problem 3 produces the following problem: 28.02/19.37 28.02/19.37 4: T: 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.37 28.02/19.37 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.37 28.02/19.37 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.37 28.02/19.37 start location: koat_start 28.02/19.37 28.02/19.37 leaf cost: 0 28.02/19.37 28.02/19.37 28.02/19.37 28.02/19.37 A polynomial rank function with 28.02/19.37 28.02/19.37 Pol(f48) = 1 28.02/19.37 28.02/19.37 Pol(f37) = 1 28.02/19.37 28.02/19.37 Pol(f43) = 1 28.02/19.37 28.02/19.37 Pol(f29) = 1 28.02/19.37 28.02/19.37 Pol(f35) = 1 28.02/19.37 28.02/19.37 Pol(f0) = 1 28.02/19.37 28.02/19.37 Pol(f22) = 1 28.02/19.37 28.02/19.37 Pol(f12) = 1 28.02/19.37 28.02/19.37 Pol(f58) = 0 28.02/19.37 28.02/19.37 Pol(start) = 1 28.02/19.37 28.02/19.37 Pol(koat_start) = 1 28.02/19.37 28.02/19.37 orients all transitions weakly and the transition 28.02/19.37 28.02/19.37 f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.37 28.02/19.37 strictly and produces the following problem: 28.02/19.37 28.02/19.37 5: T: 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.37 28.02/19.37 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 A polynomial rank function with 28.02/19.38 28.02/19.38 Pol(f48) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f37) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f43) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f29) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f35) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f0) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f22) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f12) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(f58) = V_1 - V_5 28.02/19.38 28.02/19.38 Pol(start) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 Pol(koat_start) = V_1 - V_5 + 1 28.02/19.38 28.02/19.38 orients all transitions weakly and the transitions 28.02/19.38 28.02/19.38 f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 strictly and produces the following problem: 28.02/19.38 28.02/19.38 6: T: 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Repeatedly propagating knowledge in problem 6 produces the following problem: 28.02/19.38 28.02/19.38 7: T: 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 A polynomial rank function with 28.02/19.38 28.02/19.38 Pol(f48) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f37) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f43) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f29) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f35) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f0) = V_1 - V_2 28.02/19.38 28.02/19.38 Pol(f22) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f12) = V_1 - V_2 - 1 28.02/19.38 28.02/19.38 Pol(f58) = V_1 - V_2 28.02/19.38 28.02/19.38 Pol(start) = V_1 - V_2 28.02/19.38 28.02/19.38 Pol(koat_start) = V_1 - V_2 28.02/19.38 28.02/19.38 orients all transitions weakly and the transition 28.02/19.38 28.02/19.38 f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 strictly and produces the following problem: 28.02/19.38 28.02/19.38 8: T: 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Repeatedly propagating knowledge in problem 8 produces the following problem: 28.02/19.38 28.02/19.38 9: T: 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 A polynomial rank function with 28.02/19.38 28.02/19.38 Pol(f48) = 1 28.02/19.38 28.02/19.38 Pol(f37) = 1 28.02/19.38 28.02/19.38 Pol(f43) = 1 28.02/19.38 28.02/19.38 Pol(f0) = 0 28.02/19.38 28.02/19.38 and size complexities 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 192 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 4*ar_0 + 4*ar_4 + 192 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-2) = 0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ i >= 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-1) = ? 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ]", 0-4) = 4*ar_0 + 4*ar_4 + 48 28.02/19.38 28.02/19.38 orients the transitions 28.02/19.38 28.02/19.38 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 weakly and the transition 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 strictly and produces the following problem: 28.02/19.38 28.02/19.38 10: T: 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Applied AI with 'oct' on problem 10 to obtain the following invariants: 28.02/19.38 28.02/19.38 For symbol f12: X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f22: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f29: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f35: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f37: -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f43: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 For symbol f48: -X_4 + X_5 - 1 >= 0 /\ -X_2 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_1 - X_4 >= 0 /\ X_1 - X_2 - 1 >= 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 This yielded the following problem: 28.02/19.38 28.02/19.38 11: T: 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Testing for unsatisfiable constraints removes the following transition from problem 11: 28.02/19.38 28.02/19.38 f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 ] 28.02/19.38 28.02/19.38 We thus obtain the following problem: 28.02/19.38 28.02/19.38 12: T: 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: ?, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 A polynomial rank function with 28.02/19.38 28.02/19.38 Pol(f48) = 3*V_1 - 3*V_4 + 1 28.02/19.38 28.02/19.38 Pol(f37) = 3*V_1 - 3*V_4 + 3 28.02/19.38 28.02/19.38 Pol(f43) = 3*V_1 - 3*V_4 + 2 28.02/19.38 28.02/19.38 and size complexities 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\\ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_3 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 64691683493 28.02/19.38 28.02/19.38 S("f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ 0 >= i + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 /\\ i >= 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 2812681891 28.02/19.38 28.02/19.38 S("f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 122290517 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_3 >= ar_1 + 1 /\\ ar_4 >= ar_0 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ 0 >= ar_2 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 >= 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-2) = 0 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 1487908720339 28.02/19.38 28.02/19.38 S("f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\\ -ar_0 + ar_4 - 1 >= 0 /\\ ar_0 - ar_1 - 1 >= 0 /\\ ar_2 = 0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 5316979 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= j ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-3) = 3*ar_0 + 3*ar_4 + 54 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_0 >= ar_4 /\\ i >= k + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 28.02/19.38 28.02/19.38 S("f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_4 >= ar_0 + 1 /\\ ar_1 = ar_3 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 10051 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-2) = 0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-3) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ]", 0-4) = 3*ar_0 + 3*ar_4 + 18 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = 23*ar_0 + 23*ar_1 + 23*ar_4 + 231173 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ? 28.02/19.38 28.02/19.38 S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = 3*ar_0 + 3*ar_4 + 54 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3 28.02/19.38 28.02/19.38 S("start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3 28.02/19.38 28.02/19.38 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4 28.02/19.38 28.02/19.38 orients the transitions 28.02/19.38 28.02/19.38 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 weakly and the transitions 28.02/19.38 28.02/19.38 f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 strictly and produces the following problem: 28.02/19.38 28.02/19.38 13: T: 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) 28.02/19.38 28.02/19.38 (Comp: 1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f58(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_1, Cost: 1) f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, 0, ar_1, ar_4)) [ ar_0 >= ar_1 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 3*ar_0 + ar_1 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_1, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 /\ ar_1 = ar_3 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, j, ar_4, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= k + 1 ] 28.02/19.38 28.02/19.38 (Comp: ar_0 + ar_4 + 1, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f12(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_4 /\ i >= j ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, 0, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 = 0 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 7*ar_0 + 6*ar_4 + ar_1 + 6, Cost: 1) f35(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= ar_2 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_1 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 2*ar_0 + 2*ar_4 + 2, Cost: 1) f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= ar_3 + 1 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f29(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 15*ar_0 + 13*ar_4 + 2*ar_1 + 13, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_3 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 ] 28.02/19.38 28.02/19.38 (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ i >= 1 ] 28.02/19.38 28.02/19.38 (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f37(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_0 >= ar_3 /\ 0 >= i + 1 ] 28.02/19.38 28.02/19.38 (Comp: 4*ar_0 + 4*ar_4 + 4, Cost: 1) f29(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f35(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f43(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f48(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 (Comp: 1008*ar_0^2 + 1830*ar_0*ar_4 + 1110*ar_0*ar_1 + 966*ar_1*ar_4 + 138*ar_1^2 + 828*ar_4^2 + 62492166255144*ar_0 + 8927452322868*ar_1 + 53564713933068*ar_4 + 53564713932240, Cost: 1) f48(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ -ar_3 + ar_4 - 1 >= 0 /\ -ar_1 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 1 >= 0 /\ ar_0 - ar_3 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_0 + 1 ] 28.02/19.38 28.02/19.38 start location: koat_start 28.02/19.38 28.02/19.38 leaf cost: 0 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Complexity upper bound 312460831275774*ar_0 + 44637261614347*ar_1 + 267823569665387*ar_4 + 5040*ar_0^2 + 9150*ar_0*ar_4 + 5550*ar_0*ar_1 + 4830*ar_1*ar_4 + 690*ar_1^2 + 4140*ar_4^2 + 267823569661249 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Time: 0.798 sec (SMT: 0.582 sec) 28.02/19.38 28.02/19.38 28.02/19.38 ---------------------------------------- 28.02/19.38 28.02/19.38 (2) 28.02/19.38 BOUNDS(1, n^2) 28.02/19.38 28.02/19.38 ---------------------------------------- 28.02/19.38 28.02/19.38 (3) Loat Proof (FINISHED) 28.02/19.38 28.02/19.38 28.02/19.38 ### Pre-processing the ITS problem ### 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Initial linear ITS problem 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 21: f0 -> f58 : [ B>=A ], cost: 1 28.02/19.38 28.02/19.38 1: f12 -> f12 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 28.02/19.38 28.02/19.38 2: f12 -> f12 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 17: f22 -> f29 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 16: f29 -> f35 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D && 0>=1+free_7 ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D && free_9>=1 ], cost: 1 28.02/19.38 28.02/19.38 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Removed unreachable and leaf rules: 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 1: f12 -> f12 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 28.02/19.38 28.02/19.38 2: f12 -> f12 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 17: f22 -> f29 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 16: f29 -> f35 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D && 0>=1+free_7 ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D && free_9>=1 ], cost: 1 28.02/19.38 28.02/19.38 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Simplified all rules, resulting in: 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 1: f12 -> f12 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 28.02/19.38 28.02/19.38 2: f12 -> f12 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 17: f22 -> f29 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 16: f29 -> f35 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 ### Simplification by acceleration and chaining ### 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 1. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 1: f12 -> f12 : E'=1+E, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1 28.02/19.38 28.02/19.38 2: f12 -> f12 : C'=free_3, D'=E, E'=1+E, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 1 with metering function 1+A-E, yielding the new rule 23. 28.02/19.38 28.02/19.38 Accelerated rule 2 with metering function 1+A-E, yielding the new rule 24. 28.02/19.38 28.02/19.38 Removing the simple loops: 1 2. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 2. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 3: f22 -> f22 : E'=1+E, H'=free_5, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 3 with metering function 1+A-E, yielding the new rule 25. 28.02/19.38 28.02/19.38 Removing the simple loops: 3. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 3. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 4: f29 -> f29 : E'=1+E, H'=free_6, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 4 with metering function 1+A-E, yielding the new rule 26. 28.02/19.38 28.02/19.38 Removing the simple loops: 4. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 5. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 11: f37 -> f37 : D'=1+D, H'=0, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 11 with metering function 1-D+A, yielding the new rule 27. 28.02/19.38 28.02/19.38 Removing the simple loops: 11. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 6. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 9: f43 -> f43 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 9 with metering function 1+A-E, yielding the new rule 28. 28.02/19.38 28.02/19.38 Removing the simple loops: 9. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 7. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 10: f48 -> f48 : E'=1+E, [ A>=E ], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 10 with metering function 1+A-E, yielding the new rule 29. 28.02/19.38 28.02/19.38 Removing the simple loops: 10. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated all simple loops using metering functions (where possible): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 23: f12 -> f12 : E'=1+A, F'=free_1, G'=free, [ A>=E && free>=free_1 ], cost: 1+A-E 28.02/19.38 28.02/19.38 24: f12 -> f12 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=E && free_2>=1+free_4 ], cost: 1+A-E 28.02/19.38 28.02/19.38 17: f22 -> f29 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 25: f22 -> f22 : E'=1+A, H'=free_5, [ A>=E ], cost: 1+A-E 28.02/19.38 28.02/19.38 16: f29 -> f35 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 26: f29 -> f29 : E'=1+A, H'=free_6, [ A>=E ], cost: 1+A-E 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 27: f37 -> f37 : D'=1+A, H'=0, [ A>=D ], cost: 1-D+A 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 28: f43 -> f43 : E'=1+A, [ A>=E ], cost: 1+A-E 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 29: f48 -> f48 : E'=1+A, [ A>=E ], cost: 1+A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Chained accelerated rules (with incoming rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 30: f0 -> f12 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 31: f0 -> f12 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 17: f22 -> f29 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 16: f29 -> f35 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 35: f37 -> f43 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 2+A-E 28.02/19.38 28.02/19.38 36: f37 -> f43 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 2+A-E 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on linear paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 0: f0 -> f12 : C'=0, D'=B, [ A>=1+B ], cost: 1 28.02/19.38 28.02/19.38 30: f0 -> f12 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 31: f0 -> f12 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 18: f12 -> f35 : D'=B, [ E>=1+A && B==D ], cost: 1 28.02/19.38 28.02/19.38 19: f12 -> f22 : [ B>=1+D && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 20: f12 -> f22 : [ D>=1+B && E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 37: f22 -> f35 : [ E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 7: f37 -> f43 : H'=free_8, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 8: f37 -> f43 : H'=free_10, [ A>=D ], cost: 1 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 35: f37 -> f43 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 2+A-E 28.02/19.38 28.02/19.38 36: f37 -> f43 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 2+A-E 28.02/19.38 28.02/19.38 14: f43 -> f48 : [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on tree-shaped paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 38: f0 -> f35 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 39: f0 -> f35 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 40: f0 -> f22 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 37: f22 -> f35 : [ E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 43: f37 -> f48 : H'=free_8, [ A>=D && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 44: f37 -> f48 : H'=free_10, [ A>=D && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 45: f37 -> f48 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 3+A-E 28.02/19.38 28.02/19.38 46: f37 -> f48 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 3+A-E 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on linear paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 38: f0 -> f35 : C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 39: f0 -> f35 : C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 47: f0 -> f35 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 5+A-E 28.02/19.38 28.02/19.38 5: f35 -> f37 : [ 0>=1+C ], cost: 1 28.02/19.38 28.02/19.38 6: f35 -> f37 : [ C>=1 ], cost: 1 28.02/19.38 28.02/19.38 12: f35 -> f0 : B'=1+B, C'=0, [ C==0 ], cost: 1 28.02/19.38 28.02/19.38 32: f35 -> f37 : D'=1+A, H'=0, [ 0>=1+C && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 33: f35 -> f37 : D'=1+A, H'=0, [ C>=1 && A>=D ], cost: 2-D+A 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 43: f37 -> f48 : H'=free_8, [ A>=D && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 44: f37 -> f48 : H'=free_10, [ A>=D && E>=1+A ], cost: 2 28.02/19.38 28.02/19.38 45: f37 -> f48 : E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 3+A-E 28.02/19.38 28.02/19.38 46: f37 -> f48 : E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 3+A-E 28.02/19.38 28.02/19.38 13: f48 -> f37 : D'=1+D, [ E>=1+A ], cost: 1 28.02/19.38 28.02/19.38 34: f48 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 1-D+A 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on tree-shaped paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 50: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 28.02/19.38 28.02/19.38 51: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 28.02/19.38 28.02/19.38 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E 28.02/19.38 28.02/19.38 53: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 28.02/19.38 28.02/19.38 54: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 56: f37 -> f37 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 57: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 28.02/19.38 28.02/19.38 58: f37 -> f37 : D'=1+D, H'=free_10, [ A>=D && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 28.02/19.38 28.02/19.38 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 61: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 28.02/19.38 28.02/19.38 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Applied pruning (of leafs and parallel rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 50: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 28.02/19.38 28.02/19.38 51: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 28.02/19.38 28.02/19.38 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3==0 ], cost: 6+A-E 28.02/19.38 28.02/19.38 53: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 28.02/19.38 28.02/19.38 54: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 56: f37 -> f37 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 28.02/19.38 28.02/19.38 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 0. 28.02/19.38 28.02/19.38 Simplified some of the simple loops (and removed duplicate rules). 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 48: f0 -> f0 : B'=1+B, C'=0, D'=B, [ A>=1+B && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 48 with metering function A-B, yielding the new rule 64. 28.02/19.38 28.02/19.38 Found no metering function for rule 49. 28.02/19.38 28.02/19.38 Found no metering function for rule 52. 28.02/19.38 28.02/19.38 Removing the simple loops: 48. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 5. 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 56: f37 -> f37 : D'=1+D, H'=free_8, [ A>=D && E>=1+A ], cost: 3 28.02/19.38 28.02/19.38 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 28.02/19.38 28.02/19.38 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated rule 56 with metering function 1-D+A, yielding the new rule 65. 28.02/19.38 28.02/19.38 Found no metering function for rule 59. 28.02/19.38 28.02/19.38 Found no metering function for rule 60. 28.02/19.38 28.02/19.38 Found no metering function for rule 62. 28.02/19.38 28.02/19.38 Found no metering function for rule 63. 28.02/19.38 28.02/19.38 Removing the simple loops: 56. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated all simple loops using metering functions (where possible): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 49: f0 -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 50: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 28.02/19.38 28.02/19.38 51: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 28.02/19.38 28.02/19.38 52: f0 -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 6+A-E 28.02/19.38 28.02/19.38 53: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 28.02/19.38 28.02/19.38 54: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 64: f0 -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 3*A-3*B 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 59: f37 -> f37 : D'=1+A, H'=0, [ E>=1+A && A>=1+D ], cost: 3-D+A 28.02/19.38 28.02/19.38 60: f37 -> f37 : D'=1+D, E'=1+A, H'=free_8, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 62: f37 -> f37 : D'=1+D, E'=1+A, H'=free_10, [ A>=D && A>=E ], cost: 4+A-E 28.02/19.38 28.02/19.38 63: f37 -> f37 : D'=1+A, E'=1+A, H'=0, [ A>=E && A>=1+D ], cost: 4-D+2*A-E 28.02/19.38 28.02/19.38 65: f37 -> f37 : D'=1+A, H'=free_8, [ A>=D && E>=1+A ], cost: 3-3*D+3*A 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Chained accelerated rules (with incoming rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 50: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 28.02/19.38 28.02/19.38 51: f0 -> f37 : C'=free_3, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 28.02/19.38 28.02/19.38 53: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 28.02/19.38 28.02/19.38 54: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 72: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 73: f0 -> f37 : C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 28.02/19.38 28.02/19.38 15: f37 -> f0 : B'=1+B, [ D>=1+A ], cost: 1 28.02/19.38 28.02/19.38 66: f37 -> f0 : B'=2+B, C'=0, D'=1+B, E'=1+A, F'=free_1, G'=free, [ D>=1+A && A>=2+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 68: f37 -> f0 : B'=2+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ D>=1+A && A>=2+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 70: f37 -> f0 : B'=A, C'=0, D'=-1+A, [ D>=1+A && A>=2+B && E>=1+A ], cost: -2+3*A-3*B 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on tree-shaped paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 74: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 28.02/19.38 28.02/19.38 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 28.02/19.38 28.02/19.38 76: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 8+A-E 28.02/19.38 28.02/19.38 77: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && free_3>=1 && A>=2+B ], cost: 5+4*A-E-3*B 28.02/19.38 28.02/19.38 78: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 28.02/19.38 28.02/19.38 80: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 81: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && free_3>=1 && A>=2+B ], cost: 7+4*A-E-3*B 28.02/19.38 28.02/19.38 82: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 6+A-E 28.02/19.38 28.02/19.38 83: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 6+A-E 28.02/19.38 28.02/19.38 84: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 7+A-E 28.02/19.38 28.02/19.38 85: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 7+A-E 28.02/19.38 28.02/19.38 86: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 87: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Applied pruning (of leafs and parallel rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 74: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 28.02/19.38 28.02/19.38 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 5+4*A-E-3*B 28.02/19.38 28.02/19.38 78: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && 0>=1+free_3 && A>=2+B ], cost: 7+4*A-E-3*B 28.02/19.38 28.02/19.38 80: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 86: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 87: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerating simple loops of location 0. 28.02/19.38 28.02/19.38 Simplified some of the simple loops (and removed duplicate rules). 28.02/19.38 28.02/19.38 Accelerating the following rules: 28.02/19.38 28.02/19.38 74: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 28.02/19.38 28.02/19.38 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B 28.02/19.38 28.02/19.38 78: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 7+4*A-E-3*B 28.02/19.38 28.02/19.38 80: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Found no metering function for rule 74. 28.02/19.38 28.02/19.38 Found no metering function for rule 75. 28.02/19.38 28.02/19.38 Found no metering function for rule 78. 28.02/19.38 28.02/19.38 Found no metering function for rule 79. 28.02/19.38 28.02/19.38 Found no metering function for rule 80. 28.02/19.38 28.02/19.38 Removing the simple loops:. 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Accelerated all simple loops using metering functions (where possible): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 74: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 8+A-E 28.02/19.38 28.02/19.38 75: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 5+4*A-E-3*B 28.02/19.38 28.02/19.38 78: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 79: f0 -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 7+4*A-E-3*B 28.02/19.38 28.02/19.38 80: f0 -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 86: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 87: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Chained accelerated rules (with incoming rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 41: f0 -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 2+A-E 28.02/19.38 28.02/19.38 42: f0 -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 2+A-E 28.02/19.38 28.02/19.38 55: f0 -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 86: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 87: f0 -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 9+A-E 28.02/19.38 28.02/19.38 22: start -> f0 : [], cost: 1 28.02/19.38 28.02/19.38 67: start -> f0 : B'=1+B, C'=0, D'=B, E'=1+A, F'=free_1, G'=free, [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 69: start -> f0 : B'=1+B, C'=0, D'=A, E'=1+A, F'=free_2, G'=free_4, [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 71: start -> f0 : B'=A, C'=0, D'=-1+A, [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 88: start -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 89: start -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=0, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B 28.02/19.38 28.02/19.38 90: start -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 28.02/19.38 28.02/19.38 91: start -> f0 : B'=A, C'=0, D'=-1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 8+4*A-E-3*B 28.02/19.38 28.02/19.38 92: start -> f0 : B'=1+B, C'=free_3, D'=1+A, E'=1+A, F'=free_2, G'=free_4, H'=free_8, [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Eliminated locations (on tree-shaped paths): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 93: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 94: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 28.02/19.38 28.02/19.38 95: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 96: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 97: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 101: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 9+A-E 28.02/19.38 28.02/19.38 102: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 6+4*A-E-3*B 28.02/19.38 28.02/19.38 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 28.02/19.38 28.02/19.38 104: start -> [22] : [ A>=E && free_2>=1+free_4 && A>=2+B ], cost: 8+4*A-E-3*B 28.02/19.38 28.02/19.38 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Applied pruning (of leafs and parallel rules): 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 93: start -> [16] : [ A>=1+B && A>=E && free>=free_1 ], cost: 3+A-E 28.02/19.38 28.02/19.38 94: start -> [16] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 3+A-E 28.02/19.38 28.02/19.38 95: start -> [17] : [ A>=1+B && A>=E && free>=free_1 ], cost: 4+A-E 28.02/19.38 28.02/19.38 96: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 10+A-E 28.02/19.38 28.02/19.38 97: start -> [20] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 10+A-E 28.02/19.38 28.02/19.38 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 28.02/19.38 28.02/19.38 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 ### Computing asymptotic complexity ### 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Fully simplified ITS problem 28.02/19.38 28.02/19.38 Start location: start 28.02/19.38 28.02/19.38 98: start -> [22] : [ A>=1+B && A>=E && free>=free_1 ], cost: 5+A-E 28.02/19.38 28.02/19.38 99: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 ], cost: 7+A-E 28.02/19.38 28.02/19.38 100: start -> [22] : [ A>=1+B && E>=1+A ], cost: 1+3*A-3*B 28.02/19.38 28.02/19.38 103: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && 0>=1+free_3 ], cost: 11+A-E 28.02/19.38 28.02/19.38 105: start -> [22] : [ A>=1+B && A>=E && free_2>=1+free_4 && free_3>=1 ], cost: 11+A-E 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Computing asymptotic complexity for rule 98 28.02/19.38 28.02/19.38 Solved the limit problem by the following transformations: 28.02/19.38 28.02/19.38 Created initial limit problem: 28.02/19.38 28.02/19.38 1+free-free_1 (+/+!), 5+A-E (+), 1+A-E (+/+!), A-B (+/+!) [not solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 applying transformation rule (C) using substitution {A==1+B} 28.02/19.38 28.02/19.38 resulting limit problem: 28.02/19.38 28.02/19.38 1 (+/+!), 6-E+B (+), 1+free-free_1 (+/+!), 2-E+B (+/+!) [not solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 applying transformation rule (C) using substitution {A==E} 28.02/19.38 28.02/19.38 resulting limit problem: 28.02/19.38 28.02/19.38 1 (+/+!), 6-E+B (+), 1+free-free_1 (+/+!), 2-E+B (+/+!) [not solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 applying transformation rule (C) using substitution {free==free_1} 28.02/19.38 28.02/19.38 resulting limit problem: 28.02/19.38 28.02/19.38 1 (+/+!), 6-E+B (+), 2-E+B (+/+!) [not solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 applying transformation rule (B), deleting 1 (+/+!) 28.02/19.38 28.02/19.38 resulting limit problem: 28.02/19.38 28.02/19.38 6-E+B (+), 2-E+B (+/+!) [not solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 removing all constraints (solved by SMT) 28.02/19.38 28.02/19.38 resulting limit problem: [solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 applying transformation rule (C) using substitution {E==-n,B==0} 28.02/19.38 28.02/19.38 resulting limit problem: 28.02/19.38 28.02/19.38 [solved] 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Solution: 28.02/19.38 28.02/19.38 free / 0 28.02/19.38 28.02/19.38 free_1 / 0 28.02/19.38 28.02/19.38 A / 1 28.02/19.38 28.02/19.38 E / -n 28.02/19.38 28.02/19.38 B / 0 28.02/19.38 28.02/19.38 Resulting cost 6+n has complexity: Poly(n^1) 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Found new complexity Poly(n^1). 28.02/19.38 28.02/19.38 28.02/19.38 28.02/19.38 Obtained the following overall complexity (w.r.t. the length of the input n): 28.02/19.39 28.02/19.39 Complexity: Poly(n^1) 28.02/19.39 28.02/19.39 Cpx degree: 1 28.02/19.39 28.02/19.39 Solved cost: 6+n 28.02/19.39 28.02/19.39 Rule cost: 5+A-E 28.02/19.39 28.02/19.39 Rule guard: [ A>=1+B && A>=E && free>=free_1 ] 28.02/19.39 28.02/19.39 28.02/19.39 28.02/19.39 WORST_CASE(Omega(n^1),?) 28.02/19.39 28.02/19.39 28.02/19.39 ---------------------------------------- 28.02/19.39 28.02/19.39 (4) 28.02/19.39 BOUNDS(n^1, INF) 28.02/19.41 EOF