3.64/1.70	WORST_CASE(?, O(1))
3.64/1.71	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.64/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.64/1.71	
3.64/1.71	
3.64/1.71	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.64/1.71	
3.64/1.71	(0) CpxIntTrs
3.64/1.71	(1) Koat Proof [FINISHED, 102 ms]
3.64/1.71	(2) BOUNDS(1, 1)
3.64/1.71	
3.64/1.71	
3.64/1.71	----------------------------------------
3.64/1.71	
3.64/1.71	(0)
3.64/1.71	Obligation:
3.64/1.71	Complexity Int TRS consisting of the following rules:
3.64/1.71	f0(A, B, C) -> Com_1(f9(0, D, 0)) :|: TRUE
3.64/1.71	f9(A, B, C) -> Com_1(f9(A, B, C + 1)) :|: 49 >= C
3.64/1.71	f17(A, B, C) -> Com_1(f17(A + 1, B, C)) :|: 49 >= A
3.64/1.71	f17(A, B, C) -> Com_1(f24(A, B, C)) :|: A >= 50
3.64/1.71	f9(A, B, C) -> Com_1(f17(0, B, C)) :|: C >= 50
3.64/1.71	
3.64/1.71	The start-symbols are:[f0_3]
3.64/1.71	
3.64/1.71	
3.64/1.71	----------------------------------------
3.64/1.71	
3.64/1.71	(1) Koat Proof (FINISHED)
3.64/1.71	YES(?, 105)
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	Initial complexity problem:
3.64/1.71	
3.64/1.71	1:	T:
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f9(0, d, 0))
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71		start location:	koat_start
3.64/1.71	
3.64/1.71		leaf cost:	0
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.64/1.71	
3.64/1.71	2:	T:
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f9(0, d, 0))
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71		start location:	koat_start
3.64/1.71	
3.64/1.71		leaf cost:	0
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	A polynomial rank function with
3.64/1.71	
3.64/1.71		Pol(f0) = 2
3.64/1.71	
3.64/1.71		Pol(f9) = 2
3.64/1.71	
3.64/1.71		Pol(f17) = 1
3.64/1.71	
3.64/1.71		Pol(f24) = 0
3.64/1.71	
3.64/1.71		Pol(koat_start) = 2
3.64/1.71	
3.64/1.71	orients all transitions weakly and the transitions
3.64/1.71	
3.64/1.71		f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71		f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71	strictly and produces the following problem:
3.64/1.71	
3.64/1.71	3:	T:
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f9(0, d, 0))
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71		start location:	koat_start
3.64/1.71	
3.64/1.71		leaf cost:	0
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	A polynomial rank function with
3.64/1.71	
3.64/1.71		Pol(f0) = 50
3.64/1.71	
3.64/1.71		Pol(f9) = -V_3 + 50
3.64/1.71	
3.64/1.71		Pol(f17) = -V_3
3.64/1.71	
3.64/1.71		Pol(f24) = -V_3
3.64/1.71	
3.64/1.71		Pol(koat_start) = 50
3.64/1.71	
3.64/1.71	orients all transitions weakly and the transition
3.64/1.71	
3.64/1.71		f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71	strictly and produces the following problem:
3.64/1.71	
3.64/1.71	4:	T:
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2) -> Com_1(f9(0, d, 0))
3.64/1.71	
3.64/1.71			(Comp: 50, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)     f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)     f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)     f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71		start location:	koat_start
3.64/1.71	
3.64/1.71		leaf cost:	0
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	A polynomial rank function with
3.64/1.71	
3.64/1.71		Pol(f0) = 50
3.64/1.71	
3.64/1.71		Pol(f9) = 50
3.64/1.71	
3.64/1.71		Pol(f17) = -V_1 + 50
3.64/1.71	
3.64/1.71		Pol(f24) = -V_1
3.64/1.71	
3.64/1.71		Pol(koat_start) = 50
3.64/1.71	
3.64/1.71	orients all transitions weakly and the transition
3.64/1.71	
3.64/1.71		f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71	strictly and produces the following problem:
3.64/1.71	
3.64/1.71	5:	T:
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2) -> Com_1(f9(0, d, 0))
3.64/1.71	
3.64/1.71			(Comp: 50, Cost: 1)    f9(ar_0, ar_1, ar_2) -> Com_1(f9(ar_0, ar_1, ar_2 + 1)) [ 49 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: 50, Cost: 1)    f17(ar_0, ar_1, ar_2) -> Com_1(f17(ar_0 + 1, ar_1, ar_2)) [ 49 >= ar_0 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)     f17(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1, ar_2)) [ ar_0 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 2, Cost: 1)     f9(ar_0, ar_1, ar_2) -> Com_1(f17(0, ar_1, ar_2)) [ ar_2 >= 50 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71		start location:	koat_start
3.64/1.71	
3.64/1.71		leaf cost:	0
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	Complexity upper bound 105
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	Time: 0.086 sec (SMT: 0.079 sec)
3.64/1.71	
3.64/1.71	
3.64/1.71	----------------------------------------
3.64/1.71	
3.64/1.71	(2)
3.64/1.71	BOUNDS(1, 1)
3.64/1.74	EOF