3.32/1.66	WORST_CASE(?, O(1))
3.32/1.67	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.32/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.32/1.67	
3.32/1.67	
3.32/1.67	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.32/1.67	
3.32/1.67	(0) CpxIntTrs
3.32/1.67	(1) Koat Proof [FINISHED, 4 ms]
3.32/1.67	(2) BOUNDS(1, 1)
3.32/1.67	
3.32/1.67	
3.32/1.67	----------------------------------------
3.32/1.67	
3.32/1.67	(0)
3.32/1.67	Obligation:
3.32/1.67	Complexity Int TRS consisting of the following rules:
3.32/1.67	f12(A, B, C, D, E) -> Com_1(f11(A, B, C, D, E)) :|: TRUE
3.32/1.67	f28(A, B, C, D, E) -> Com_1(f20(A, 1, A, 1, A)) :|: A >= 1
3.32/1.67	
3.32/1.67	The start-symbols are:[f28_5]
3.32/1.67	
3.32/1.67	
3.32/1.67	----------------------------------------
3.32/1.67	
3.32/1.67	(1) Koat Proof (FINISHED)
3.32/1.67	YES(?, 1)
3.32/1.67	
3.32/1.67	
3.32/1.67	
3.32/1.67	Initial complexity problem:
3.32/1.67	
3.32/1.67	1:	T:
3.32/1.67	
3.32/1.67			(Comp: ?, Cost: 1)    f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f11(ar_0, ar_1, ar_2, ar_3, ar_4))
3.32/1.67	
3.32/1.67			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 1, ar_0, 1, ar_0)) [ ar_0 >= 1 ]
3.32/1.67	
3.32/1.67			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f28(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.32/1.67	
3.32/1.67		start location:	koat_start
3.32/1.67	
3.32/1.67		leaf cost:	0
3.32/1.67	
3.32/1.67	
3.32/1.67	
3.32/1.67	Testing for reachability in the complexity graph removes the following transition from problem 1:
3.32/1.67	
3.32/1.67		f12(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f11(ar_0, ar_1, ar_2, ar_3, ar_4))
3.32/1.67	
3.32/1.67	We thus obtain the following problem:
3.32/1.67	
3.32/1.67	2:	T:
3.32/1.67	
3.32/1.67			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 1, ar_0, 1, ar_0)) [ ar_0 >= 1 ]
3.32/1.67	
3.32/1.67			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f28(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.32/1.67	
3.32/1.67		start location:	koat_start
3.32/1.67	
3.32/1.67		leaf cost:	0
3.32/1.67	
3.32/1.67	
3.32/1.67	
3.32/1.67	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.32/1.67	
3.32/1.67	3:	T:
3.32/1.67	
3.32/1.67			(Comp: 1, Cost: 1)    f28(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 1, ar_0, 1, ar_0)) [ ar_0 >= 1 ]
3.32/1.67	
3.32/1.67			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f28(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.32/1.67	
3.32/1.67		start location:	koat_start
3.32/1.67	
3.32/1.67		leaf cost:	0
3.32/1.67	
3.32/1.67	
3.32/1.67	
3.32/1.67	Complexity upper bound 1
3.32/1.67	
3.32/1.67	
3.32/1.67	
3.32/1.67	Time: 0.012 sec (SMT: 0.012 sec)
3.32/1.67	
3.32/1.67	
3.32/1.67	----------------------------------------
3.32/1.67	
3.32/1.67	(2)
3.32/1.67	BOUNDS(1, 1)
3.49/1.70	EOF