3.54/1.68	WORST_CASE(?, O(1))
3.54/1.69	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.54/1.69	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.54/1.69	
3.54/1.69	
3.54/1.69	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.54/1.69	
3.54/1.69	(0) CpxIntTrs
3.54/1.69	(1) Koat Proof [FINISHED, 23 ms]
3.54/1.69	(2) BOUNDS(1, 1)
3.54/1.69	
3.54/1.69	
3.54/1.69	----------------------------------------
3.54/1.69	
3.54/1.69	(0)
3.54/1.69	Obligation:
3.54/1.69	Complexity Int TRS consisting of the following rules:
3.54/1.69	f300(A, B, C, D, E) -> Com_1(f300(-(1) + A, B, C, D, E)) :|: A >= 101 && 9 >= B
3.54/1.69	f300(A, B, C, D, E) -> Com_1(f2(A, B, 0, 0, 0)) :|: 100 >= A && 9 >= B
3.54/1.69	f300(A, B, C, D, E) -> Com_1(f2(A, B, 0, 0, 0)) :|: B >= 10
3.54/1.69	f1(A, B, C, D, E) -> Com_1(f300(1000, B, C, D, E)) :|: TRUE
3.54/1.69	
3.54/1.69	The start-symbols are:[f1_5]
3.54/1.69	
3.54/1.69	
3.54/1.69	----------------------------------------
3.54/1.69	
3.54/1.69	(1) Koat Proof (FINISHED)
3.54/1.69	YES(?, 1003)
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	Initial complexity problem:
3.54/1.69	
3.54/1.69	1:	T:
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ]
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4))
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.54/1.69	
3.54/1.69		start location:	koat_start
3.54/1.69	
3.54/1.69		leaf cost:	0
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.54/1.69	
3.54/1.69	2:	T:
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4))
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.54/1.69	
3.54/1.69		start location:	koat_start
3.54/1.69	
3.54/1.69		leaf cost:	0
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	A polynomial rank function with
3.54/1.69	
3.54/1.69		Pol(f300) = 1
3.54/1.69	
3.54/1.69		Pol(f2) = 0
3.54/1.69	
3.54/1.69		Pol(f1) = 1
3.54/1.69	
3.54/1.69		Pol(koat_start) = 1
3.54/1.69	
3.54/1.69	orients all transitions weakly and the transition
3.54/1.69	
3.54/1.69		f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69	strictly and produces the following problem:
3.54/1.69	
3.54/1.69	3:	T:
3.54/1.69	
3.54/1.69			(Comp: ?, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)    f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4))
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.54/1.69	
3.54/1.69		start location:	koat_start
3.54/1.69	
3.54/1.69		leaf cost:	0
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	A polynomial rank function with
3.54/1.69	
3.54/1.69		Pol(f300) = V_1
3.54/1.69	
3.54/1.69		Pol(f2) = V_1
3.54/1.69	
3.54/1.69		Pol(f1) = 1000
3.54/1.69	
3.54/1.69		Pol(koat_start) = 1000
3.54/1.69	
3.54/1.69	orients all transitions weakly and the transition
3.54/1.69	
3.54/1.69		f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69	strictly and produces the following problem:
3.54/1.69	
3.54/1.69	4:	T:
3.54/1.69	
3.54/1.69			(Comp: 1000, Cost: 1)    f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(ar_0 - 1, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= 101 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)       f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ 100 >= ar_0 /\ 9 >= ar_1 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)       f300(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f2(ar_0, ar_1, 0, 0, 0)) [ ar_1 >= 10 ]
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 1)       f1(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f300(1000, ar_1, ar_2, ar_3, ar_4))
3.54/1.69	
3.54/1.69			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f1(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.54/1.69	
3.54/1.69		start location:	koat_start
3.54/1.69	
3.54/1.69		leaf cost:	0
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	Complexity upper bound 1003
3.54/1.69	
3.54/1.69	
3.54/1.69	
3.54/1.69	Time: 0.061 sec (SMT: 0.054 sec)
3.54/1.69	
3.54/1.69	
3.54/1.69	----------------------------------------
3.54/1.69	
3.54/1.69	(2)
3.54/1.69	BOUNDS(1, 1)
3.58/1.71	EOF