4.92/2.16 WORST_CASE(Omega(n^1), O(n^1)) 4.92/2.17 proof of /export/starexec/sandbox/benchmark/theBenchmark.koat 4.92/2.17 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 4.92/2.17 4.92/2.17 4.92/2.17 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). 4.92/2.17 4.92/2.17 (0) CpxIntTrs 4.92/2.17 (1) Koat Proof [FINISHED, 289 ms] 4.92/2.17 (2) BOUNDS(1, n^1) 4.92/2.17 (3) Loat Proof [FINISHED, 373 ms] 4.92/2.17 (4) BOUNDS(n^1, INF) 4.92/2.17 4.92/2.17 4.92/2.17 ---------------------------------------- 4.92/2.17 4.92/2.17 (0) 4.92/2.17 Obligation: 4.92/2.17 Complexity Int TRS consisting of the following rules: 4.92/2.17 start(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: 0 >= A && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.92/2.17 start(A, B, C, D, E, F) -> Com_1(lbl6(A, B, C, D, E, F)) :|: A >= 1 && A >= C && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.92/2.17 start(A, B, C, D, E, F) -> Com_1(lbl121(A, B, C, D, B - D, F)) :|: A >= 1 && C >= A + 1 && B >= C && B <= C && D >= A && D <= A && E >= F && E <= F 4.92/2.17 lbl6(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 1 && A >= C && E >= F && E <= F && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl111(A, B, C, D, E, F) -> Com_1(cut(A, B, C, D, E, F)) :|: C >= A + 1 && A >= 2 && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl111(A, B, C, D, E, F) -> Com_1(lbl111(A, B, C, D, E - 1, F)) :|: E >= 1 && A >= E + 1 && E >= 0 && C >= E + A + 1 && A >= E + 2 && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl111(A, B, C, D, E, F) -> Com_1(lbl121(A, B, C, D, E - D, F)) :|: E >= 1 && E >= A && E >= 0 && C >= E + A + 1 && A >= E + 2 && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl121(A, B, C, D, E, F) -> Com_1(cut(A, B, C, D, E, F)) :|: C >= A + 1 && A >= 1 && C >= A && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl121(A, B, C, D, E, F) -> Com_1(lbl111(A, B, C, D, E - 1, F)) :|: E >= 1 && A >= E + 1 && C >= A + 1 && A >= 1 && E >= 0 && C >= E + A && D >= A && D <= A && B >= C && B <= C 4.92/2.17 lbl121(A, B, C, D, E, F) -> Com_1(lbl121(A, B, C, D, E - D, F)) :|: E >= 1 && E >= A && C >= A + 1 && A >= 1 && E >= 0 && C >= E + A && D >= A && D <= A && B >= C && B <= C 4.92/2.17 cut(A, B, C, D, E, F) -> Com_1(stop(A, B, C, D, E, F)) :|: A >= 1 && C >= A + 1 && E >= 0 && E <= 0 && D >= A && D <= A && B >= C && B <= C 4.92/2.17 start0(A, B, C, D, E, F) -> Com_1(start(A, C, C, A, F, F)) :|: TRUE 4.92/2.17 4.92/2.17 The start-symbols are:[start0_6] 4.92/2.17 4.92/2.17 4.92/2.17 ---------------------------------------- 4.92/2.17 4.92/2.17 (1) Koat Proof (FINISHED) 4.92/2.17 YES(?, 8*ar_2 + 25) 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Initial complexity problem: 4.92/2.17 4.92/2.17 1: T: 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_4 = ar_5 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.92/2.17 4.92/2.17 start location: koat_start 4.92/2.17 4.92/2.17 leaf cost: 0 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Testing for reachability in the complexity graph removes the following transition from problem 1: 4.92/2.17 4.92/2.17 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 We thus obtain the following problem: 4.92/2.17 4.92/2.17 2: T: 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_4 = ar_5 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.92/2.17 4.92/2.17 start location: koat_start 4.92/2.17 4.92/2.17 leaf cost: 0 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Repeatedly propagating knowledge in problem 2 produces the following problem: 4.92/2.17 4.92/2.17 3: T: 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_4 = ar_5 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.92/2.17 4.92/2.17 start location: koat_start 4.92/2.17 4.92/2.17 leaf cost: 0 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 A polynomial rank function with 4.92/2.17 4.92/2.17 Pol(cut) = 1 4.92/2.17 4.92/2.17 Pol(stop) = 0 4.92/2.17 4.92/2.17 Pol(lbl121) = 3 4.92/2.17 4.92/2.17 Pol(lbl111) = 2 4.92/2.17 4.92/2.17 Pol(lbl6) = 0 4.92/2.17 4.92/2.17 Pol(start) = 3 4.92/2.17 4.92/2.17 Pol(start0) = 3 4.92/2.17 4.92/2.17 Pol(koat_start) = 3 4.92/2.17 4.92/2.17 orients all transitions weakly and the transitions 4.92/2.17 4.92/2.17 lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 strictly and produces the following problem: 4.92/2.17 4.92/2.17 4: T: 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: ?, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_4 = ar_5 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.92/2.17 4.92/2.17 start location: koat_start 4.92/2.17 4.92/2.17 leaf cost: 0 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 A polynomial rank function with 4.92/2.17 4.92/2.17 Pol(lbl121) = V_5 + 1 4.92/2.17 4.92/2.17 Pol(lbl111) = V_5 + 1 4.92/2.17 4.92/2.17 and size complexities 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-1) = ar_1 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-3) = ar_3 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-4) = ar_4 4.92/2.17 4.92/2.17 S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-4) = ar_5 4.92/2.17 4.92/2.17 S("start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5))", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = ar_5 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = ar_5 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-4) = ar_2 4.92/2.17 4.92/2.17 S("start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_1 = ar_2 /\\ ar_3 = ar_0 /\\ ar_4 = ar_5 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = ar_5 4.92/2.17 4.92/2.17 S("lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_0 >= ar_2 /\\ ar_4 = ar_5 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\\ ar_4 >= ar_0 /\\ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = 0 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 2 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = ar_2 4.92/2.17 4.92/2.17 S("lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\\ ar_0 >= ar_4 + 1 /\\ ar_4 >= 0 /\\ ar_2 >= ar_4 + ar_0 + 1 /\\ ar_0 >= ar_4 + 2 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = 0 4.92/2.17 4.92/2.17 S("lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\\ ar_0 >= 1 /\\ ar_2 >= ar_0 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-0) = ar_0 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-1) = ar_2 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-2) = ar_2 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-3) = ar_0 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-4) = 0 4.92/2.17 4.92/2.17 S("cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\\ ar_2 >= ar_0 + 1 /\\ ar_4 = 0 /\\ ar_3 = ar_0 /\\ ar_1 = ar_2 ]", 0-5) = ar_5 4.92/2.17 4.92/2.17 orients the transitions 4.92/2.17 4.92/2.17 lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 weakly and the transitions 4.92/2.17 4.92/2.17 lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 strictly and produces the following problem: 4.92/2.17 4.92/2.17 5: T: 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 4*ar_2 + 4, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 + 1 /\ ar_0 >= ar_4 + 2 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl111(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(cut(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= 2 /\ ar_4 = 0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 4*ar_2 + 4, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_4 - ar_3, ar_5)) [ ar_4 >= 1 /\ ar_4 >= ar_0 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 3, Cost: 1) lbl121(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl111(ar_0, ar_1, ar_2, ar_3, ar_4 - 1, ar_5)) [ ar_4 >= 1 /\ ar_0 >= ar_4 + 1 /\ ar_2 >= ar_0 + 1 /\ ar_0 >= 1 /\ ar_4 >= 0 /\ ar_2 >= ar_4 + ar_0 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_4 = ar_5 /\ ar_3 = ar_0 /\ ar_1 = ar_2 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl121(ar_0, ar_1, ar_2, ar_3, ar_1 - ar_3, ar_5)) [ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(lbl6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ ar_0 >= 1 /\ ar_0 >= ar_2 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 >= ar_0 /\ ar_1 = ar_2 /\ ar_3 = ar_0 /\ ar_4 = ar_5 ] 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 1) start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start(ar_0, ar_2, ar_2, ar_0, ar_5, ar_5)) 4.92/2.17 4.92/2.17 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5)) [ 0 <= 0 ] 4.92/2.17 4.92/2.17 start location: koat_start 4.92/2.17 4.92/2.17 leaf cost: 0 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Complexity upper bound 8*ar_2 + 25 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Time: 0.321 sec (SMT: 0.259 sec) 4.92/2.17 4.92/2.17 4.92/2.17 ---------------------------------------- 4.92/2.17 4.92/2.17 (2) 4.92/2.17 BOUNDS(1, n^1) 4.92/2.17 4.92/2.17 ---------------------------------------- 4.92/2.17 4.92/2.17 (3) Loat Proof (FINISHED) 4.92/2.17 4.92/2.17 4.92/2.17 ### Pre-processing the ITS problem ### 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Initial linear ITS problem 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 0: start -> stop : [ 0>=A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 1: start -> lbl6 : [ A>=1 && A>=C && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 3: lbl6 -> stop : [ A>=1 && A>=C && E==F && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 4: lbl111 -> cut : [ C>=1+A && A>=2 && E==0 && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 5: lbl111 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && E>=0 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 6: lbl111 -> lbl121 : E'=-D+E, [ E>=1 && E>=A && E>=0 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 7: lbl121 -> cut : [ C>=1+A && A>=1 && C>=A && E==0 && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 9: lbl121 -> lbl121 : E'=-D+E, [ E>=1 && E>=A && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 10: cut -> stop : [ A>=1 && C>=1+A && E==0 && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Removed unreachable and leaf rules: 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 5: lbl111 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && E>=0 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 6: lbl111 -> lbl121 : E'=-D+E, [ E>=1 && E>=A && E>=0 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 9: lbl121 -> lbl121 : E'=-D+E, [ E>=1 && E>=A && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Removed rules with unsatisfiable guard: 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 5: lbl111 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && E>=0 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 9: lbl121 -> lbl121 : E'=-D+E, [ E>=1 && E>=A && C>=1+A && A>=1 && E>=0 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Simplified all rules, resulting in: 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 5: lbl111 -> lbl111 : E'=-1+E, [ E>=1 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 9: lbl121 -> lbl121 : E'=-D+E, [ E>=A && C>=1+A && A>=1 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 ### Simplification by acceleration and chaining ### 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Accelerating simple loops of location 2. 4.92/2.17 4.92/2.17 Accelerating the following rules: 4.92/2.17 4.92/2.17 5: lbl111 -> lbl111 : E'=-1+E, [ E>=1 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Accelerated rule 5 with metering function E, yielding the new rule 12. 4.92/2.17 4.92/2.17 Removing the simple loops: 5. 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Accelerating simple loops of location 3. 4.92/2.17 4.92/2.17 Accelerating the following rules: 4.92/2.17 4.92/2.17 9: lbl121 -> lbl121 : E'=-D+E, [ E>=A && C>=1+A && A>=1 && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Accelerated rule 9 with metering function -D+A, yielding the new rule 13. 4.92/2.17 4.92/2.17 Removing the simple loops: 9. 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Accelerated all simple loops using metering functions (where possible): 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 12: lbl111 -> lbl111 : E'=0, [ E>=1 && C>=1+A+E && A>=2+E && D==A && B==C ], cost: E 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 13: lbl121 -> lbl121 : E'=E+(D-A)*D, [ E>=A && C>=1+A && A>=1 && C>=A+E && D==A && B==C && -D+A>=1 ], cost: -D+A 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Chained accelerated rules (with incoming rules): 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 8: lbl121 -> lbl111 : E'=-1+E, [ E>=1 && A>=1+E && C>=1+A && C>=A+E && D==A && B==C ], cost: 1 4.92/2.17 4.92/2.17 14: lbl121 -> lbl111 : E'=0, [ A>=1+E && C>=1+A && C>=A+E && D==A && B==C && -1+E>=1 ], cost: E 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Removed unreachable locations (and leaf rules with constant cost): 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 2: start -> lbl121 : E'=-D+B, [ A>=1 && C>=1+A && B==C && D==A && E==F ], cost: 1 4.92/2.17 4.92/2.17 14: lbl121 -> lbl111 : E'=0, [ A>=1+E && C>=1+A && C>=A+E && D==A && B==C && -1+E>=1 ], cost: E 4.92/2.17 4.92/2.17 11: start0 -> start : B'=C, D'=A, E'=F, [], cost: 1 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Eliminated locations (on linear paths): 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 16: start0 -> lbl111 : B'=C, D'=A, E'=0, [ A>=1 && A>=1+C-A && -1+C-A>=1 ], cost: 2+C-A 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 ### Computing asymptotic complexity ### 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Fully simplified ITS problem 4.92/2.17 4.92/2.17 Start location: start0 4.92/2.17 4.92/2.17 16: start0 -> lbl111 : B'=C, D'=A, E'=0, [ A>=1 && A>=1+C-A && -1+C-A>=1 ], cost: 2+C-A 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Computing asymptotic complexity for rule 16 4.92/2.17 4.92/2.17 Simplified the guard: 4.92/2.17 4.92/2.17 16: start0 -> lbl111 : B'=C, D'=A, E'=0, [ A>=1+C-A && -1+C-A>=1 ], cost: 2+C-A 4.92/2.17 4.92/2.17 Solved the limit problem by the following transformations: 4.92/2.17 4.92/2.17 Created initial limit problem: 4.92/2.17 4.92/2.17 -1+C-A (+/+!), 2+C-A (+), -C+2*A (+/+!) [not solved] 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 removing all constraints (solved by SMT) 4.92/2.17 4.92/2.17 resulting limit problem: [solved] 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 applying transformation rule (C) using substitution {C==3*n,A==2*n} 4.92/2.17 4.92/2.17 resulting limit problem: 4.92/2.17 4.92/2.17 [solved] 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Solution: 4.92/2.17 4.92/2.17 C / 3*n 4.92/2.17 4.92/2.17 A / 2*n 4.92/2.17 4.92/2.17 Resulting cost 2+n has complexity: Poly(n^1) 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Found new complexity Poly(n^1). 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 Obtained the following overall complexity (w.r.t. the length of the input n): 4.92/2.17 4.92/2.17 Complexity: Poly(n^1) 4.92/2.17 4.92/2.17 Cpx degree: 1 4.92/2.17 4.92/2.17 Solved cost: 2+n 4.92/2.17 4.92/2.17 Rule cost: 2+C-A 4.92/2.17 4.92/2.17 Rule guard: [ A>=1+C-A && -1+C-A>=1 ] 4.92/2.17 4.92/2.17 4.92/2.17 4.92/2.17 WORST_CASE(Omega(n^1),?) 4.92/2.17 4.92/2.17 4.92/2.17 ---------------------------------------- 4.92/2.17 4.92/2.17 (4) 4.92/2.17 BOUNDS(n^1, INF) 4.92/2.20 EOF