3.64/1.72	WORST_CASE(?, O(1))
3.64/1.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.64/1.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.64/1.72	
3.64/1.72	
3.64/1.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.64/1.72	
3.64/1.72	(0) CpxIntTrs
3.64/1.72	(1) Koat Proof [FINISHED, 7 ms]
3.64/1.72	(2) BOUNDS(1, 1)
3.64/1.72	
3.64/1.72	
3.64/1.72	----------------------------------------
3.64/1.72	
3.64/1.72	(0)
3.64/1.72	Obligation:
3.64/1.72	Complexity Int TRS consisting of the following rules:
3.64/1.72	f0(A, B, C, D, E, F, G, H, I) -> Com_1(f7(30, 30, 1, 0, 2, F, G, H, I)) :|: TRUE
3.64/1.72	f7(A, B, C, D, E, F, G, H, I) -> Com_1(f7(A, B, C + D, C, E + 1, C, G, H, I)) :|: B >= E
3.64/1.72	f7(A, B, C, D, E, F, G, H, I) -> Com_1(f19(A, B, C, D, E, F, C, C, C)) :|: E >= 1 + B
3.64/1.72	
3.64/1.72	The start-symbols are:[f0_9]
3.64/1.72	
3.64/1.72	
3.64/1.72	----------------------------------------
3.64/1.72	
3.64/1.72	(1) Koat Proof (FINISHED)
3.64/1.72	YES(?, 31)
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	Initial complexity problem:
3.64/1.72	
3.64/1.72	1:	T:
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(30, 30, 1, 0, 2, ar_5, ar_6, ar_7, ar_8))
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(ar_0, ar_1, ar_2 + ar_3, ar_2, ar_4 + 1, ar_2, ar_6, ar_7, ar_8)) [ ar_1 >= ar_4 ]
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_2, ar_2)) [ ar_4 >= ar_1 + 1 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ]
3.64/1.72	
3.64/1.72		start location:	koat_start
3.64/1.72	
3.64/1.72		leaf cost:	0
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.64/1.72	
3.64/1.72	2:	T:
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(30, 30, 1, 0, 2, ar_5, ar_6, ar_7, ar_8))
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(ar_0, ar_1, ar_2 + ar_3, ar_2, ar_4 + 1, ar_2, ar_6, ar_7, ar_8)) [ ar_1 >= ar_4 ]
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_2, ar_2)) [ ar_4 >= ar_1 + 1 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ]
3.64/1.72	
3.64/1.72		start location:	koat_start
3.64/1.72	
3.64/1.72		leaf cost:	0
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	A polynomial rank function with
3.64/1.72	
3.64/1.72		Pol(f0) = 1
3.64/1.72	
3.64/1.72		Pol(f7) = 1
3.64/1.72	
3.64/1.72		Pol(f19) = 0
3.64/1.72	
3.64/1.72		Pol(koat_start) = 1
3.64/1.72	
3.64/1.72	orients all transitions weakly and the transition
3.64/1.72	
3.64/1.72		f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_2, ar_2)) [ ar_4 >= ar_1 + 1 ]
3.64/1.72	
3.64/1.72	strictly and produces the following problem:
3.64/1.72	
3.64/1.72	3:	T:
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(30, 30, 1, 0, 2, ar_5, ar_6, ar_7, ar_8))
3.64/1.72	
3.64/1.72			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(ar_0, ar_1, ar_2 + ar_3, ar_2, ar_4 + 1, ar_2, ar_6, ar_7, ar_8)) [ ar_1 >= ar_4 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_2, ar_2)) [ ar_4 >= ar_1 + 1 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ]
3.64/1.72	
3.64/1.72		start location:	koat_start
3.64/1.72	
3.64/1.72		leaf cost:	0
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	A polynomial rank function with
3.64/1.72	
3.64/1.72		Pol(f0) = 29
3.64/1.72	
3.64/1.72		Pol(f7) = V_2 - V_5 + 1
3.64/1.72	
3.64/1.72		Pol(f19) = V_2 - V_5
3.64/1.72	
3.64/1.72		Pol(koat_start) = 29
3.64/1.72	
3.64/1.72	orients all transitions weakly and the transition
3.64/1.72	
3.64/1.72		f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(ar_0, ar_1, ar_2 + ar_3, ar_2, ar_4 + 1, ar_2, ar_6, ar_7, ar_8)) [ ar_1 >= ar_4 ]
3.64/1.72	
3.64/1.72	strictly and produces the following problem:
3.64/1.72	
3.64/1.72	4:	T:
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(30, 30, 1, 0, 2, ar_5, ar_6, ar_7, ar_8))
3.64/1.72	
3.64/1.72			(Comp: 29, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f7(ar_0, ar_1, ar_2 + ar_3, ar_2, ar_4 + 1, ar_2, ar_6, ar_7, ar_8)) [ ar_1 >= ar_4 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_2, ar_2, ar_2)) [ ar_4 >= ar_1 + 1 ]
3.64/1.72	
3.64/1.72			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8)) [ 0 <= 0 ]
3.64/1.72	
3.64/1.72		start location:	koat_start
3.64/1.72	
3.64/1.72		leaf cost:	0
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	Complexity upper bound 31
3.64/1.72	
3.64/1.72	
3.64/1.72	
3.64/1.72	Time: 0.094 sec (SMT: 0.086 sec)
3.64/1.72	
3.64/1.72	
3.64/1.72	----------------------------------------
3.64/1.72	
3.64/1.72	(2)
3.64/1.72	BOUNDS(1, 1)
3.64/1.75	EOF