5.19/2.26	WORST_CASE(Omega(n^1), O(n^1))
5.19/2.27	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.19/2.27	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.19/2.27	
5.19/2.27	
5.19/2.27	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.19/2.27	
5.19/2.27	(0) CpxIntTrs
5.19/2.27	(1) Koat Proof [FINISHED, 551 ms]
5.19/2.27	(2) BOUNDS(1, n^1)
5.19/2.27	(3) Loat Proof [FINISHED, 437 ms]
5.19/2.27	(4) BOUNDS(n^1, INF)
5.19/2.27	
5.19/2.27	
5.19/2.27	----------------------------------------
5.19/2.27	
5.19/2.27	(0)
5.19/2.27	Obligation:
5.19/2.27	Complexity Int TRS consisting of the following rules:
5.19/2.27	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, 1, F, G, H, I, J)) :|: A >= 1 && B >= C + 1 && D >= B && D <= B && E >= F && E <= F && G >= C && G <= C && H >= I && H <= I && J >= A && J <= A
5.19/2.27	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl71(A, B, C, 1 + D, 1, F, G, H, I, J)) :|: A >= 1 && C >= B && D >= B && D <= B && E >= F && E <= F && G >= C && G <= C && H >= I && H <= I && J >= A && J <= A
5.19/2.27	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, -(1), F, G, H, I, J)) :|: B >= C + 1 && 0 >= A && D >= B && D <= B && E >= F && E <= F && G >= C && G <= C && H >= I && H <= I && J >= A && J <= A
5.19/2.27	start(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, 1 + D, -(1), F, G, H, I, J)) :|: C >= B && 0 >= A && D >= B && D <= B && E >= F && E <= F && G >= C && G <= C && H >= I && H <= I && J >= A && J <= A
5.19/2.27	lbl71(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: C >= B && A >= 1 && D >= C + 1 && D <= C + 1 && E >= 1 && E <= 1 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	lbl71(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl71(A, B, C, E + D, E, F, G, H, I, J)) :|: A >= 1 && C >= D && D >= B + 1 && C + 1 >= D && E >= 1 && E <= 1 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	lbl71(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D - E, E, F, G, H, I, J)) :|: C >= D && 0 >= A && D >= B + 1 && C + 1 >= D && A >= 1 && E >= 1 && E <= 1 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(stop(A, B, C, D, E, F, G, H, I, J)) :|: 0 >= A && C >= B && D >= C + 1 && D <= C + 1 && E + 1 >= 0 && E + 1 <= 0 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl71(A, B, C, E + D, E, F, G, H, I, J)) :|: A >= 1 && C >= D && 0 >= A && D >= B + 1 && C + 1 >= D && E + 1 >= 0 && E + 1 <= 0 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	lbl81(A, B, C, D, E, F, G, H, I, J) -> Com_1(lbl81(A, B, C, D - E, E, F, G, H, I, J)) :|: C >= D && 0 >= A && D >= B + 1 && C + 1 >= D && E + 1 >= 0 && E + 1 <= 0 && J >= A && J <= A && H >= I && H <= I && G >= C && G <= C
5.19/2.27	start0(A, B, C, D, E, F, G, H, I, J) -> Com_1(start(A, B, C, B, F, F, C, I, I, A)) :|: TRUE
5.19/2.27	
5.19/2.27	The start-symbols are:[start0_10]
5.19/2.27	
5.19/2.27	
5.19/2.27	----------------------------------------
5.19/2.27	
5.19/2.27	(1) Koat Proof (FINISHED)
5.19/2.27	YES(?, 2*ar_1 + 2*ar_2 + 7)
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Initial complexity problem:
5.19/2.27	
5.19/2.27	1:	T:
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3 + 1, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 >= ar_2 + 1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 + 1, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_0 >= 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start(ar_0, ar_1, ar_2, ar_1, ar_5, ar_5, ar_2, ar_8, ar_8, ar_0))
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
5.19/2.27	
5.19/2.27		start location:	koat_start
5.19/2.27	
5.19/2.27		leaf cost:	0
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Testing for reachability in the complexity graph removes the following transitions from problem 1:
5.19/2.27	
5.19/2.27		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_0 >= 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27		lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27	We thus obtain the following problem:
5.19/2.27	
5.19/2.27	2:	T:
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 + 1, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 >= ar_2 + 1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3 + 1, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start(ar_0, ar_1, ar_2, ar_1, ar_5, ar_5, ar_2, ar_8, ar_8, ar_0))
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
5.19/2.27	
5.19/2.27		start location:	koat_start
5.19/2.27	
5.19/2.27		leaf cost:	0
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.19/2.27	
5.19/2.27	3:	T:
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 + 1, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 >= ar_2 + 1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3 + 1, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start(ar_0, ar_1, ar_2, ar_1, ar_5, ar_5, ar_2, ar_8, ar_8, ar_0))
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
5.19/2.27	
5.19/2.27		start location:	koat_start
5.19/2.27	
5.19/2.27		leaf cost:	0
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	A polynomial rank function with
5.19/2.27	
5.19/2.27		Pol(lbl81) = 1
5.19/2.27	
5.19/2.27		Pol(stop) = 0
5.19/2.27	
5.19/2.27		Pol(lbl71) = 1
5.19/2.27	
5.19/2.27		Pol(start) = 1
5.19/2.27	
5.19/2.27		Pol(start0) = 1
5.19/2.27	
5.19/2.27		Pol(koat_start) = 1
5.19/2.27	
5.19/2.27	orients all transitions weakly and the transitions
5.19/2.27	
5.19/2.27		lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27	strictly and produces the following problem:
5.19/2.27	
5.19/2.27	4:	T:
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ?, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 + 1, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 >= ar_2 + 1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3 + 1, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start(ar_0, ar_1, ar_2, ar_1, ar_5, ar_5, ar_2, ar_8, ar_8, ar_0))
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
5.19/2.27	
5.19/2.27		start location:	koat_start
5.19/2.27	
5.19/2.27		leaf cost:	0
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	A polynomial rank function with
5.19/2.27	
5.19/2.27		Pol(lbl81) = -V_4 - V_5 + V_7
5.19/2.27	
5.19/2.27		Pol(stop) = V_3 - V_4
5.19/2.27	
5.19/2.27		Pol(lbl71) = -V_4 + V_7 + 1
5.19/2.27	
5.19/2.27		Pol(start) = -V_2 + V_7
5.19/2.27	
5.19/2.27		Pol(start0) = -V_2 + V_3
5.19/2.27	
5.19/2.27		Pol(koat_start) = -V_2 + V_3
5.19/2.27	
5.19/2.27	orients all transitions weakly and the transitions
5.19/2.27	
5.19/2.27		lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27		lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27	strictly and produces the following problem:
5.19/2.27	
5.19/2.27	5:	T:
5.19/2.27	
5.19/2.27			(Comp: ar_1 + ar_2, Cost: 1)    lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 - ar_4, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_3 /\ 0 >= ar_0 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              lbl81(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 >= ar_0 /\ ar_2 >= ar_1 /\ ar_3 = ar_2 + 1 /\ ar_4 + 1 = 0 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: ar_1 + ar_2, Cost: 1)    lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_4 + ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_3 /\ ar_3 >= ar_1 + 1 /\ ar_2 + 1 >= ar_3 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              lbl71(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ ar_0 >= 1 /\ ar_3 = ar_2 + 1 /\ ar_4 = 1 /\ ar_9 = ar_0 /\ ar_7 = ar_8 /\ ar_6 = ar_2 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl81(ar_0, ar_1, ar_2, ar_3 + 1, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_2 >= ar_1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, -1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_1 >= ar_2 + 1 /\ 0 >= ar_0 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(lbl71(ar_0, ar_1, ar_2, ar_3 + 1, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_2 >= ar_1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(stop(ar_0, ar_1, ar_2, ar_3, 1, ar_5, ar_6, ar_7, ar_8, ar_9)) [ ar_0 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_3 = ar_1 /\ ar_4 = ar_5 /\ ar_6 = ar_2 /\ ar_7 = ar_8 /\ ar_9 = ar_0 ]
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 1)              start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start(ar_0, ar_1, ar_2, ar_1, ar_5, ar_5, ar_2, ar_8, ar_8, ar_0))
5.19/2.27	
5.19/2.27			(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
5.19/2.27	
5.19/2.27		start location:	koat_start
5.19/2.27	
5.19/2.27		leaf cost:	0
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Complexity upper bound 2*ar_1 + 2*ar_2 + 7
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Time: 0.458 sec (SMT: 0.362 sec)
5.19/2.27	
5.19/2.27	
5.19/2.27	----------------------------------------
5.19/2.27	
5.19/2.27	(2)
5.19/2.27	BOUNDS(1, n^1)
5.19/2.27	
5.19/2.27	----------------------------------------
5.19/2.27	
5.19/2.27	(3) Loat Proof (FINISHED)
5.19/2.27	
5.19/2.27	
5.19/2.27	### Pre-processing the ITS problem ###
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Initial linear ITS problem
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      0: start -> stop : E'=1, [ A>=1 && B>=1+C && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      2: start -> stop : E'=-1, [ B>=1+C && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      4: lbl71 -> stop : [ C>=B && A>=1 && D==1+C && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      5: lbl71 -> lbl71 : D'=D+E, [ A>=1 && C>=D && D>=1+B && 1+C>=D && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      6: lbl71 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+C>=D && A>=1 && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      7: lbl81 -> stop : [ 0>=A && C>=B && D==1+C && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      8: lbl81 -> lbl71 : D'=D+E, [ A>=1 && C>=D && 0>=A && D>=1+B && 1+C>=D && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      9: lbl81 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+C>=D && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Removed unreachable and leaf rules:
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      5: lbl71 -> lbl71 : D'=D+E, [ A>=1 && C>=D && D>=1+B && 1+C>=D && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      6: lbl71 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+C>=D && A>=1 && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      8: lbl81 -> lbl71 : D'=D+E, [ A>=1 && C>=D && 0>=A && D>=1+B && 1+C>=D && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      9: lbl81 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+C>=D && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Removed rules with unsatisfiable guard:
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      5: lbl71 -> lbl71 : D'=D+E, [ A>=1 && C>=D && D>=1+B && 1+C>=D && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      9: lbl81 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+C>=D && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Simplified all rules, resulting in:
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      5: lbl71 -> lbl71 : D'=D+E, [ A>=1 && C>=D && D>=1+B && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	      9: lbl81 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	### Simplification by acceleration and chaining ###
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Accelerating simple loops of location 1.
5.19/2.27	
5.19/2.27	   Accelerating the following rules:
5.19/2.27	
5.19/2.27	      5: lbl71 -> lbl71 : D'=D+E, [ A>=1 && C>=D && D>=1+B && E==1 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	   Accelerated rule 5 with metering function 2+C-D-E, yielding the new rule 11.
5.19/2.27	
5.19/2.27	   Removing the simple loops: 5.
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Accelerating simple loops of location 2.
5.19/2.27	
5.19/2.27	   Accelerating the following rules:
5.19/2.27	
5.19/2.27	      9: lbl81 -> lbl81 : D'=D-E, [ C>=D && 0>=A && D>=1+B && 1+E==0 && J==A && H==Q && G==C ], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	   Accelerated rule 9 with metering function C-D-E, yielding the new rule 12.
5.19/2.27	
5.19/2.27	   Removing the simple loops: 9.
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Accelerated all simple loops using metering functions (where possible):
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	     11: lbl71 -> lbl71 : D'=(2+C-D-E)*E+D, [ A>=1 && C>=D && D>=1+B && E==1 && J==A && H==Q && G==C && 2+C-D-E>=1 ], cost: 2+C-D-E
5.19/2.27	
5.19/2.27	     12: lbl81 -> lbl81 : D'=-(C-D-E)*E+D, [ C>=D && 0>=A && D>=1+B && 1+E==0 && J==A && H==Q && G==C && C-D-E>=1 ], cost: C-D-E
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Chained accelerated rules (with incoming rules):
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	      1: start -> lbl71 : D'=1+D, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	      3: start -> lbl81 : D'=1+D, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A ], cost: 1
5.19/2.27	
5.19/2.27	     13: start -> lbl71 : D'=1+C, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A && C>=1+D ], cost: 1+C-D
5.19/2.27	
5.19/2.27	     14: start -> lbl81 : D'=1+C, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A && C>=1+D ], cost: 1+C-D
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Removed unreachable locations (and leaf rules with constant cost):
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	     13: start -> lbl71 : D'=1+C, E'=1, [ A>=1 && C>=B && D==B && E==F && G==C && H==Q && J==A && C>=1+D ], cost: 1+C-D
5.19/2.27	
5.19/2.27	     14: start -> lbl81 : D'=1+C, E'=-1, [ C>=B && 0>=A && D==B && E==F && G==C && H==Q && J==A && C>=1+D ], cost: 1+C-D
5.19/2.27	
5.19/2.27	     10: start0 -> start : D'=B, E'=F, G'=C, H'=Q, J'=A, [], cost: 1
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Eliminated locations (on tree-shaped paths):
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	     15: start0 -> lbl71 : D'=1+C, E'=1, G'=C, H'=Q, J'=A, [ A>=1 && C>=1+B ], cost: 2+C-B
5.19/2.27	
5.19/2.27	     16: start0 -> lbl81 : D'=1+C, E'=-1, G'=C, H'=Q, J'=A, [ 0>=A && C>=1+B ], cost: 2+C-B
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	### Computing asymptotic complexity ###
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Fully simplified ITS problem
5.19/2.27	
5.19/2.27	   Start location: start0
5.19/2.27	
5.19/2.27	     15: start0 -> lbl71 : D'=1+C, E'=1, G'=C, H'=Q, J'=A, [ A>=1 && C>=1+B ], cost: 2+C-B
5.19/2.27	
5.19/2.27	     16: start0 -> lbl81 : D'=1+C, E'=-1, G'=C, H'=Q, J'=A, [ 0>=A && C>=1+B ], cost: 2+C-B
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Computing asymptotic complexity for rule 15
5.19/2.27	
5.19/2.27	   Solved the limit problem by the following transformations:
5.19/2.27	
5.19/2.27	      Created initial limit problem:
5.19/2.27	
5.19/2.27	      2+C-B (+), C-B (+/+!), A (+/+!) [not solved]
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	      removing all constraints (solved by SMT)
5.19/2.27	
5.19/2.27	      resulting limit problem: [solved]
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	      applying transformation rule (C) using substitution {C==0,A==n,B==-n}
5.19/2.27	
5.19/2.27	      resulting limit problem:
5.19/2.27	
5.19/2.27	      [solved]
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	   Solution:
5.19/2.27	
5.19/2.27	      C / 0
5.19/2.27	
5.19/2.27	      A / n
5.19/2.27	
5.19/2.27	      B / -n
5.19/2.27	
5.19/2.27	   Resulting cost 2+n has complexity: Poly(n^1)
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Found new complexity Poly(n^1).
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	Obtained the following overall complexity (w.r.t. the length of the input n):
5.19/2.27	
5.19/2.27	   Complexity:  Poly(n^1)
5.19/2.27	
5.19/2.27	   Cpx degree:  1
5.19/2.27	
5.19/2.27	   Solved cost: 2+n
5.19/2.27	
5.19/2.27	   Rule cost:   2+C-B
5.19/2.27	
5.19/2.27	   Rule guard:  [ A>=1 && C>=1+B ]
5.19/2.27	
5.19/2.27	
5.19/2.27	
5.19/2.27	WORST_CASE(Omega(n^1),?)
5.19/2.27	
5.19/2.27	
5.19/2.27	----------------------------------------
5.19/2.27	
5.19/2.27	(4)
5.19/2.27	BOUNDS(n^1, INF)
5.35/2.29	EOF