3.40/1.74	WORST_CASE(?, O(1))
3.40/1.75	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
3.40/1.75	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.40/1.75	
3.40/1.75	
3.40/1.75	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.40/1.75	
3.40/1.75	(0) CpxIntTrs
3.40/1.75	(1) Koat Proof [FINISHED, 20 ms]
3.40/1.75	(2) BOUNDS(1, 1)
3.40/1.75	
3.40/1.75	
3.40/1.75	----------------------------------------
3.40/1.75	
3.40/1.75	(0)
3.40/1.75	Obligation:
3.40/1.75	Complexity Int TRS consisting of the following rules:
3.40/1.75	f0(A) -> Com_1(f3(0)) :|: TRUE
3.40/1.75	f3(A) -> Com_1(f3(A + 1)) :|: 41 >= A
3.40/1.75	f3(A) -> Com_1(f3(A + 1)) :|: 41 >= A && 0 >= B + 1
3.40/1.75	f3(A) -> Com_1(f13(A)) :|: A >= 42
3.40/1.75	
3.40/1.75	The start-symbols are:[f0_1]
3.40/1.75	
3.40/1.75	
3.40/1.75	----------------------------------------
3.40/1.75	
3.40/1.75	(1) Koat Proof (FINISHED)
3.40/1.75	YES(?, 86)
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	Initial complexity problem:
3.40/1.75	
3.40/1.75	1:	T:
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f3(0))
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 ]
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 /\ 0 >= b + 1 ]
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f13(ar_0)) [ ar_0 >= 42 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.40/1.75	
3.40/1.75		start location:	koat_start
3.40/1.75	
3.40/1.75		leaf cost:	0
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.40/1.75	
3.40/1.75	2:	T:
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f3(0))
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 ]
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 /\ 0 >= b + 1 ]
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f13(ar_0)) [ ar_0 >= 42 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.40/1.75	
3.40/1.75		start location:	koat_start
3.40/1.75	
3.40/1.75		leaf cost:	0
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	A polynomial rank function with
3.40/1.75	
3.40/1.75		Pol(f0) = 1
3.40/1.75	
3.40/1.75		Pol(f3) = 1
3.40/1.75	
3.40/1.75		Pol(f13) = 0
3.40/1.75	
3.40/1.75		Pol(koat_start) = 1
3.40/1.75	
3.40/1.75	orients all transitions weakly and the transition
3.40/1.75	
3.40/1.75		f3(ar_0) -> Com_1(f13(ar_0)) [ ar_0 >= 42 ]
3.40/1.75	
3.40/1.75	strictly and produces the following problem:
3.40/1.75	
3.40/1.75	3:	T:
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f3(0))
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 ]
3.40/1.75	
3.40/1.75			(Comp: ?, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 /\ 0 >= b + 1 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 1)    f3(ar_0) -> Com_1(f13(ar_0)) [ ar_0 >= 42 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.40/1.75	
3.40/1.75		start location:	koat_start
3.40/1.75	
3.40/1.75		leaf cost:	0
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	A polynomial rank function with
3.40/1.75	
3.40/1.75		Pol(f0) = 42
3.40/1.75	
3.40/1.75		Pol(f3) = -V_1 + 42
3.40/1.75	
3.40/1.75		Pol(f13) = -V_1
3.40/1.75	
3.40/1.75		Pol(koat_start) = 42
3.40/1.75	
3.40/1.75	orients all transitions weakly and the transitions
3.40/1.75	
3.40/1.75		f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 /\ 0 >= b + 1 ]
3.40/1.75	
3.40/1.75		f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 ]
3.40/1.75	
3.40/1.75	strictly and produces the following problem:
3.40/1.75	
3.40/1.75	4:	T:
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 1)     f0(ar_0) -> Com_1(f3(0))
3.40/1.75	
3.40/1.75			(Comp: 42, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 ]
3.40/1.75	
3.40/1.75			(Comp: 42, Cost: 1)    f3(ar_0) -> Com_1(f3(ar_0 + 1)) [ 41 >= ar_0 /\ 0 >= b + 1 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 1)     f3(ar_0) -> Com_1(f13(ar_0)) [ ar_0 >= 42 ]
3.40/1.75	
3.40/1.75			(Comp: 1, Cost: 0)     koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.40/1.75	
3.40/1.75		start location:	koat_start
3.40/1.75	
3.40/1.75		leaf cost:	0
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	Complexity upper bound 86
3.40/1.75	
3.40/1.75	
3.40/1.75	
3.40/1.75	Time: 0.069 sec (SMT: 0.067 sec)
3.40/1.75	
3.40/1.75	
3.40/1.75	----------------------------------------
3.40/1.75	
3.40/1.75	(2)
3.40/1.75	BOUNDS(1, 1)
3.70/1.77	EOF