3.75/1.76	WORST_CASE(?, O(1))
3.75/1.77	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.75/1.77	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.75/1.77	
3.75/1.77	
3.75/1.77	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.75/1.77	
3.75/1.77	(0) CpxIntTrs
3.75/1.77	(1) Koat Proof [FINISHED, 67 ms]
3.75/1.77	(2) BOUNDS(1, 1)
3.75/1.77	
3.75/1.77	
3.75/1.77	----------------------------------------
3.75/1.77	
3.75/1.77	(0)
3.75/1.77	Obligation:
3.75/1.77	Complexity Int TRS consisting of the following rules:
3.75/1.77	f0(A, B, C, D, E) -> Com_1(f4(0, B, C, D, E)) :|: TRUE
3.75/1.77	f20(A, B, C, D, E) -> Com_1(f20(A, B + 1, B, D, E)) :|: 199 >= B
3.75/1.77	f20(A, B, C, D, E) -> Com_1(f31(A, B, C, D, E)) :|: B >= 200
3.75/1.77	f4(A, B, C, D, E) -> Com_1(f4(A + 1, B, C, A, A)) :|: 99 >= A
3.75/1.77	f4(A, B, C, D, E) -> Com_1(f20(A, 100, C, D, E)) :|: A >= 100
3.75/1.77	
3.75/1.77	The start-symbols are:[f0_5]
3.75/1.77	
3.75/1.77	
3.75/1.77	----------------------------------------
3.75/1.77	
3.75/1.77	(1) Koat Proof (FINISHED)
3.75/1.77	YES(?, 205)
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	Initial complexity problem:
3.75/1.77	
3.75/1.77	1:	T:
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(0, ar_1, ar_2, ar_3, ar_4))
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.75/1.77	
3.75/1.77		start location:	koat_start
3.75/1.77	
3.75/1.77		leaf cost:	0
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.75/1.77	
3.75/1.77	2:	T:
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(0, ar_1, ar_2, ar_3, ar_4))
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.75/1.77	
3.75/1.77		start location:	koat_start
3.75/1.77	
3.75/1.77		leaf cost:	0
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	A polynomial rank function with
3.75/1.77	
3.75/1.77		Pol(f0) = 2
3.75/1.77	
3.75/1.77		Pol(f4) = 2
3.75/1.77	
3.75/1.77		Pol(f20) = 1
3.75/1.77	
3.75/1.77		Pol(f31) = 0
3.75/1.77	
3.75/1.77		Pol(koat_start) = 2
3.75/1.77	
3.75/1.77	orients all transitions weakly and the transitions
3.75/1.77	
3.75/1.77		f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77		f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77	strictly and produces the following problem:
3.75/1.77	
3.75/1.77	3:	T:
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(0, ar_1, ar_2, ar_3, ar_4))
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.75/1.77	
3.75/1.77		start location:	koat_start
3.75/1.77	
3.75/1.77		leaf cost:	0
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	A polynomial rank function with
3.75/1.77	
3.75/1.77		Pol(f0) = 100
3.75/1.77	
3.75/1.77		Pol(f4) = 100
3.75/1.77	
3.75/1.77		Pol(f20) = -V_2 + 200
3.75/1.77	
3.75/1.77		Pol(f31) = -V_2
3.75/1.77	
3.75/1.77		Pol(koat_start) = 100
3.75/1.77	
3.75/1.77	orients all transitions weakly and the transition
3.75/1.77	
3.75/1.77		f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77	strictly and produces the following problem:
3.75/1.77	
3.75/1.77	4:	T:
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(0, ar_1, ar_2, ar_3, ar_4))
3.75/1.77	
3.75/1.77			(Comp: 100, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)      f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77			(Comp: ?, Cost: 1)      f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)      f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.75/1.77	
3.75/1.77		start location:	koat_start
3.75/1.77	
3.75/1.77		leaf cost:	0
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	A polynomial rank function with
3.75/1.77	
3.75/1.77		Pol(f0) = 100
3.75/1.77	
3.75/1.77		Pol(f4) = -V_1 + 100
3.75/1.77	
3.75/1.77		Pol(f20) = -V_1
3.75/1.77	
3.75/1.77		Pol(f31) = -V_1
3.75/1.77	
3.75/1.77		Pol(koat_start) = 100
3.75/1.77	
3.75/1.77	orients all transitions weakly and the transition
3.75/1.77	
3.75/1.77		f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77	strictly and produces the following problem:
3.75/1.77	
3.75/1.77	5:	T:
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(0, ar_1, ar_2, ar_3, ar_4))
3.75/1.77	
3.75/1.77			(Comp: 100, Cost: 1)    f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)      f20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.75/1.77	
3.75/1.77			(Comp: 100, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f4(ar_0 + 1, ar_1, ar_2, ar_0, ar_0)) [ 99 >= ar_0 ]
3.75/1.77	
3.75/1.77			(Comp: 2, Cost: 1)      f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f20(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.75/1.77	
3.75/1.77			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
3.75/1.77	
3.75/1.77		start location:	koat_start
3.75/1.77	
3.75/1.77		leaf cost:	0
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	Complexity upper bound 205
3.75/1.77	
3.75/1.77	
3.75/1.77	
3.75/1.77	Time: 0.110 sec (SMT: 0.100 sec)
3.75/1.77	
3.75/1.77	
3.75/1.77	----------------------------------------
3.75/1.77	
3.75/1.77	(2)
3.75/1.77	BOUNDS(1, 1)
3.75/1.79	EOF