3.18/1.64	WORST_CASE(?, O(1))
3.18/1.65	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.18/1.65	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.18/1.65	
3.18/1.65	
3.18/1.65	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.18/1.65	
3.18/1.65	(0) CpxIntTrs
3.18/1.65	(1) Koat Proof [FINISHED, 17 ms]
3.18/1.65	(2) BOUNDS(1, 1)
3.18/1.65	
3.18/1.65	
3.18/1.65	----------------------------------------
3.18/1.65	
3.18/1.65	(0)
3.18/1.65	Obligation:
3.18/1.65	Complexity Int TRS consisting of the following rules:
3.18/1.65	f0(A, B) -> Com_1(f3(1, B)) :|: TRUE
3.18/1.65	f3(A, B) -> Com_1(f3(A + 1, 10 - A)) :|: 10 >= A
3.18/1.65	f3(A, B) -> Com_1(f10(A, B)) :|: A >= 11
3.18/1.65	
3.18/1.65	The start-symbols are:[f0_2]
3.18/1.65	
3.18/1.65	
3.18/1.65	----------------------------------------
3.18/1.65	
3.18/1.65	(1) Koat Proof (FINISHED)
3.18/1.65	YES(?, 12)
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	Initial complexity problem:
3.18/1.65	
3.18/1.65	1:	T:
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f3(1, ar_1))
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f3(ar_0 + 1, -ar_0 + 10)) [ 10 >= ar_0 ]
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f10(ar_0, ar_1)) [ ar_0 >= 11 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.18/1.65	
3.18/1.65		start location:	koat_start
3.18/1.65	
3.18/1.65		leaf cost:	0
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.18/1.65	
3.18/1.65	2:	T:
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f3(1, ar_1))
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f3(ar_0 + 1, -ar_0 + 10)) [ 10 >= ar_0 ]
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f10(ar_0, ar_1)) [ ar_0 >= 11 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.18/1.65	
3.18/1.65		start location:	koat_start
3.18/1.65	
3.18/1.65		leaf cost:	0
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	A polynomial rank function with
3.18/1.65	
3.18/1.65		Pol(f0) = 1
3.18/1.65	
3.18/1.65		Pol(f3) = 1
3.18/1.65	
3.18/1.65		Pol(f10) = 0
3.18/1.65	
3.18/1.65		Pol(koat_start) = 1
3.18/1.65	
3.18/1.65	orients all transitions weakly and the transition
3.18/1.65	
3.18/1.65		f3(ar_0, ar_1) -> Com_1(f10(ar_0, ar_1)) [ ar_0 >= 11 ]
3.18/1.65	
3.18/1.65	strictly and produces the following problem:
3.18/1.65	
3.18/1.65	3:	T:
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 1)    f0(ar_0, ar_1) -> Com_1(f3(1, ar_1))
3.18/1.65	
3.18/1.65			(Comp: ?, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f3(ar_0 + 1, -ar_0 + 10)) [ 10 >= ar_0 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f10(ar_0, ar_1)) [ ar_0 >= 11 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.18/1.65	
3.18/1.65		start location:	koat_start
3.18/1.65	
3.18/1.65		leaf cost:	0
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	A polynomial rank function with
3.18/1.65	
3.18/1.65		Pol(f0) = 10
3.18/1.65	
3.18/1.65		Pol(f3) = -V_1 + 11
3.18/1.65	
3.18/1.65		Pol(f10) = -V_1
3.18/1.65	
3.18/1.65		Pol(koat_start) = 10
3.18/1.65	
3.18/1.65	orients all transitions weakly and the transition
3.18/1.65	
3.18/1.65		f3(ar_0, ar_1) -> Com_1(f3(ar_0 + 1, -ar_0 + 10)) [ 10 >= ar_0 ]
3.18/1.65	
3.18/1.65	strictly and produces the following problem:
3.18/1.65	
3.18/1.65	4:	T:
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 1)     f0(ar_0, ar_1) -> Com_1(f3(1, ar_1))
3.18/1.65	
3.18/1.65			(Comp: 10, Cost: 1)    f3(ar_0, ar_1) -> Com_1(f3(ar_0 + 1, -ar_0 + 10)) [ 10 >= ar_0 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 1)     f3(ar_0, ar_1) -> Com_1(f10(ar_0, ar_1)) [ ar_0 >= 11 ]
3.18/1.65	
3.18/1.65			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1) -> Com_1(f0(ar_0, ar_1)) [ 0 <= 0 ]
3.18/1.65	
3.18/1.65		start location:	koat_start
3.18/1.65	
3.18/1.65		leaf cost:	0
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	Complexity upper bound 12
3.18/1.65	
3.18/1.65	
3.18/1.65	
3.18/1.65	Time: 0.056 sec (SMT: 0.053 sec)
3.18/1.65	
3.18/1.65	
3.18/1.65	----------------------------------------
3.18/1.65	
3.18/1.65	(2)
3.18/1.65	BOUNDS(1, 1)
3.49/1.68	EOF