3.34/1.77	WORST_CASE(?, O(1))
3.34/1.78	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.34/1.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.34/1.78	
3.34/1.78	
3.34/1.78	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.34/1.78	
3.34/1.78	(0) CpxIntTrs
3.34/1.78	(1) Koat Proof [FINISHED, 31 ms]
3.34/1.78	(2) BOUNDS(1, 1)
3.34/1.78	
3.34/1.78	
3.34/1.78	----------------------------------------
3.34/1.78	
3.34/1.78	(0)
3.34/1.78	Obligation:
3.34/1.78	Complexity Int TRS consisting of the following rules:
3.34/1.78	f0(A, B, C, D, E) -> Com_1(f4(0, B, C, D, E)) :|: TRUE
3.34/1.78	f24(A, B, C, D, E) -> Com_1(f24(A, B + 1, B, D, E)) :|: 199 >= B
3.34/1.78	f24(A, B, C, D, E) -> Com_1(f37(A, B, C, D, E)) :|: B >= 200
3.34/1.78	f4(A, B, C, D, E) -> Com_1(f4(A + 1, B, C, A, A)) :|: 99 >= A
3.34/1.78	f4(A, B, C, D, E) -> Com_1(f24(A, 100, C, D, E)) :|: A >= 100
3.34/1.78	
3.34/1.78	The start-symbols are:[f0_5]
3.34/1.78	
3.34/1.78	
3.34/1.78	----------------------------------------
3.34/1.78	
3.34/1.78	(1) Koat Proof (FINISHED)
3.34/1.78	YES(?, 205)
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	Initial complexity problem:
3.34/1.78	
3.34/1.78	1:	T:
3.34/1.78	
3.34/1.78			(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))
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78		start location:	koat_start
3.34/1.78	
3.34/1.78		leaf cost:	0
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.34/1.78	
3.34/1.78	2:	T:
3.34/1.78	
3.34/1.78			(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))
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78		start location:	koat_start
3.34/1.78	
3.34/1.78		leaf cost:	0
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	A polynomial rank function with
3.34/1.78	
3.34/1.78		Pol(f0) = 2
3.34/1.78	
3.34/1.78		Pol(f4) = 2
3.34/1.78	
3.34/1.78		Pol(f24) = 1
3.34/1.78	
3.34/1.78		Pol(f37) = 0
3.34/1.78	
3.34/1.78		Pol(koat_start) = 2
3.34/1.78	
3.34/1.78	orients all transitions weakly and the transitions
3.34/1.78	
3.34/1.78		f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78		f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78	strictly and produces the following problem:
3.34/1.78	
3.34/1.78	3:	T:
3.34/1.78	
3.34/1.78			(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))
3.34/1.78	
3.34/1.78			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)    f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78		start location:	koat_start
3.34/1.78	
3.34/1.78		leaf cost:	0
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	A polynomial rank function with
3.34/1.78	
3.34/1.78		Pol(f0) = 100
3.34/1.78	
3.34/1.78		Pol(f4) = 100
3.34/1.78	
3.34/1.78		Pol(f24) = -V_2 + 200
3.34/1.78	
3.34/1.78		Pol(f37) = -V_2
3.34/1.78	
3.34/1.78		Pol(koat_start) = 100
3.34/1.78	
3.34/1.78	orients all transitions weakly and the transition
3.34/1.78	
3.34/1.78		f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78	strictly and produces the following problem:
3.34/1.78	
3.34/1.78	4:	T:
3.34/1.78	
3.34/1.78			(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))
3.34/1.78	
3.34/1.78			(Comp: 100, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)      f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)      f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78		start location:	koat_start
3.34/1.78	
3.34/1.78		leaf cost:	0
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	A polynomial rank function with
3.34/1.78	
3.34/1.78		Pol(f0) = 100
3.34/1.78	
3.34/1.78		Pol(f4) = -V_1 + 100
3.34/1.78	
3.34/1.78		Pol(f24) = -V_1
3.34/1.78	
3.34/1.78		Pol(f37) = -V_1
3.34/1.78	
3.34/1.78		Pol(koat_start) = 100
3.34/1.78	
3.34/1.78	orients all transitions weakly and the transition
3.34/1.78	
3.34/1.78		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 ]
3.34/1.78	
3.34/1.78	strictly and produces the following problem:
3.34/1.78	
3.34/1.78	5:	T:
3.34/1.78	
3.34/1.78			(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))
3.34/1.78	
3.34/1.78			(Comp: 100, Cost: 1)    f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, ar_1 + 1, ar_1, ar_3, ar_4)) [ 199 >= ar_1 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)      f24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f37(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 200 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78			(Comp: 2, Cost: 1)      f4(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f24(ar_0, 100, ar_2, ar_3, ar_4)) [ ar_0 >= 100 ]
3.34/1.78	
3.34/1.78			(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 ]
3.34/1.78	
3.34/1.78		start location:	koat_start
3.34/1.78	
3.34/1.78		leaf cost:	0
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	Complexity upper bound 205
3.34/1.78	
3.34/1.78	
3.34/1.78	
3.34/1.78	Time: 0.099 sec (SMT: 0.089 sec)
3.34/1.78	
3.34/1.78	
3.34/1.78	----------------------------------------
3.34/1.78	
3.34/1.78	(2)
3.34/1.78	BOUNDS(1, 1)
3.74/1.80	EOF