3.25/1.58	WORST_CASE(?, O(1))
3.25/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.25/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.25/1.59	
3.25/1.59	
3.25/1.59	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.25/1.59	
3.25/1.59	(0) CpxIntTrs
3.25/1.59	(1) Koat Proof [FINISHED, 7 ms]
3.25/1.59	(2) BOUNDS(1, 1)
3.25/1.59	
3.25/1.59	
3.25/1.59	----------------------------------------
3.25/1.59	
3.25/1.59	(0)
3.25/1.59	Obligation:
3.25/1.59	Complexity Int TRS consisting of the following rules:
3.25/1.59	start(A, B, C, D) -> Com_1(lbl41(E, B, C, D)) :|: A >= B && A <= B && C >= D && C <= D
3.25/1.59	lbl41(A, B, C, D) -> Com_1(stop(A, B, A, D)) :|: C >= D && C <= D
3.25/1.59	start0(A, B, C, D) -> Com_1(start(B, B, D, D)) :|: TRUE
3.25/1.59	
3.25/1.59	The start-symbols are:[start0_4]
3.25/1.59	
3.25/1.59	
3.25/1.59	----------------------------------------
3.25/1.59	
3.25/1.59	(1) Koat Proof (FINISHED)
3.25/1.59	YES(?, 3)
3.25/1.59	
3.25/1.59	
3.25/1.59	
3.25/1.59	Initial complexity problem:
3.25/1.59	
3.25/1.59	1:	T:
3.25/1.59	
3.25/1.59			(Comp: ?, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3) -> Com_1(lbl41(e, ar_1, ar_2, ar_3)) [ ar_0 = ar_1 /\ ar_2 = ar_3 ]
3.25/1.59	
3.25/1.59			(Comp: ?, Cost: 1)    lbl41(ar_0, ar_1, ar_2, ar_3) -> Com_1(stop(ar_0, ar_1, ar_0, ar_3)) [ ar_2 = ar_3 ]
3.25/1.59	
3.25/1.59			(Comp: ?, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3) -> Com_1(start(ar_1, ar_1, ar_3, ar_3))
3.25/1.59	
3.25/1.59			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
3.25/1.59	
3.25/1.59		start location:	koat_start
3.25/1.59	
3.25/1.59		leaf cost:	0
3.25/1.59	
3.25/1.59	
3.25/1.59	
3.25/1.59	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.25/1.59	
3.25/1.59	2:	T:
3.25/1.59	
3.25/1.59			(Comp: 1, Cost: 1)    start(ar_0, ar_1, ar_2, ar_3) -> Com_1(lbl41(e, ar_1, ar_2, ar_3)) [ ar_0 = ar_1 /\ ar_2 = ar_3 ]
3.25/1.59	
3.25/1.59			(Comp: 1, Cost: 1)    lbl41(ar_0, ar_1, ar_2, ar_3) -> Com_1(stop(ar_0, ar_1, ar_0, ar_3)) [ ar_2 = ar_3 ]
3.25/1.59	
3.25/1.59			(Comp: 1, Cost: 1)    start0(ar_0, ar_1, ar_2, ar_3) -> Com_1(start(ar_1, ar_1, ar_3, ar_3))
3.25/1.59	
3.25/1.59			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(start0(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
3.25/1.59	
3.25/1.59		start location:	koat_start
3.25/1.59	
3.25/1.59		leaf cost:	0
3.25/1.59	
3.25/1.59	
3.25/1.59	
3.25/1.59	Complexity upper bound 3
3.25/1.59	
3.25/1.59	
3.25/1.59	
3.25/1.59	Time: 0.021 sec (SMT: 0.020 sec)
3.25/1.59	
3.25/1.59	
3.25/1.59	----------------------------------------
3.25/1.59	
3.25/1.59	(2)
3.25/1.59	BOUNDS(1, 1)
3.25/1.62	EOF