3.51/1.69	WORST_CASE(?, O(1))
3.64/1.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.64/1.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.64/1.70	
3.64/1.70	
3.64/1.70	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.64/1.70	
3.64/1.70	(0) CpxIntTrs
3.64/1.70	(1) Koat Proof [FINISHED, 12 ms]
3.64/1.70	(2) BOUNDS(1, 1)
3.64/1.70	
3.64/1.70	
3.64/1.70	----------------------------------------
3.64/1.70	
3.64/1.70	(0)
3.64/1.70	Obligation:
3.64/1.70	Complexity Int TRS consisting of the following rules:
3.64/1.70	f0(A, B, C, D, E) -> Com_1(f7(F, F, 10, 0, E)) :|: TRUE
3.64/1.70	f7(A, B, C, D, E) -> Com_1(f7(A, B, C, D + 1, F)) :|: C >= D + 1
3.64/1.70	f7(A, B, C, D, E) -> Com_1(f19(A, B, C, D, E)) :|: D >= C
3.64/1.70	
3.64/1.70	The start-symbols are:[f0_5]
3.64/1.70	
3.64/1.70	
3.64/1.70	----------------------------------------
3.64/1.70	
3.64/1.70	(1) Koat Proof (FINISHED)
3.64/1.70	YES(?, 12)
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	Initial complexity problem:
3.64/1.70	
3.64/1.70	1:	T:
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(f, f, 10, 0, ar_4))
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1, ar_2, ar_3 + 1, f)) [ ar_2 >= ar_3 + 1 ]
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 0)    koat_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 ]
3.64/1.70	
3.64/1.70		start location:	koat_start
3.64/1.70	
3.64/1.70		leaf cost:	0
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.64/1.70	
3.64/1.70	2:	T:
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(f, f, 10, 0, ar_4))
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1, ar_2, ar_3 + 1, f)) [ ar_2 >= ar_3 + 1 ]
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 0)    koat_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 ]
3.64/1.70	
3.64/1.70		start location:	koat_start
3.64/1.70	
3.64/1.70		leaf cost:	0
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	A polynomial rank function with
3.64/1.70	
3.64/1.70		Pol(f0) = 1
3.64/1.70	
3.64/1.70		Pol(f7) = 1
3.64/1.70	
3.64/1.70		Pol(f19) = 0
3.64/1.70	
3.64/1.70		Pol(koat_start) = 1
3.64/1.70	
3.64/1.70	orients all transitions weakly and the transition
3.64/1.70	
3.64/1.70		f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
3.64/1.70	
3.64/1.70	strictly and produces the following problem:
3.64/1.70	
3.64/1.70	3:	T:
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(f, f, 10, 0, ar_4))
3.64/1.70	
3.64/1.70			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1, ar_2, ar_3 + 1, f)) [ ar_2 >= ar_3 + 1 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 0)    koat_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 ]
3.64/1.70	
3.64/1.70		start location:	koat_start
3.64/1.70	
3.64/1.70		leaf cost:	0
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	A polynomial rank function with
3.64/1.70	
3.64/1.70		Pol(f0) = 10
3.64/1.70	
3.64/1.70		Pol(f7) = V_3 - V_4
3.64/1.70	
3.64/1.70		Pol(f19) = V_3 - V_4
3.64/1.70	
3.64/1.70		Pol(koat_start) = 10
3.64/1.70	
3.64/1.70	orients all transitions weakly and the transition
3.64/1.70	
3.64/1.70		f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1, ar_2, ar_3 + 1, f)) [ ar_2 >= ar_3 + 1 ]
3.64/1.70	
3.64/1.70	strictly and produces the following problem:
3.64/1.70	
3.64/1.70	4:	T:
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(f, f, 10, 0, ar_4))
3.64/1.70	
3.64/1.70			(Comp: 10, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1, ar_2, ar_3 + 1, f)) [ ar_2 >= ar_3 + 1 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f19(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 ]
3.64/1.70	
3.64/1.70			(Comp: 1, Cost: 0)     koat_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 ]
3.64/1.70	
3.64/1.70		start location:	koat_start
3.64/1.70	
3.64/1.70		leaf cost:	0
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	Complexity upper bound 12
3.64/1.70	
3.64/1.70	
3.64/1.70	
3.64/1.70	Time: 0.049 sec (SMT: 0.045 sec)
3.64/1.70	
3.64/1.70	
3.64/1.70	----------------------------------------
3.64/1.70	
3.64/1.70	(2)
3.64/1.70	BOUNDS(1, 1)
3.64/1.71	EOF