3.53/1.72	WORST_CASE(?, O(1))
3.53/1.73	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.53/1.73	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.53/1.73	
3.53/1.73	
3.53/1.73	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.53/1.73	
3.53/1.73	(0) CpxIntTrs
3.53/1.73	(1) Koat Proof [FINISHED, 21 ms]
3.53/1.73	(2) BOUNDS(1, 1)
3.53/1.73	
3.53/1.73	
3.53/1.73	----------------------------------------
3.53/1.73	
3.53/1.73	(0)
3.53/1.73	Obligation:
3.53/1.73	Complexity Int TRS consisting of the following rules:
3.53/1.73	f0(A, B, C, D, E, F, G, H, I, J) -> Com_1(f5(K, 0, 0, D, E, F, G, H, I, J)) :|: TRUE
3.53/1.73	f5(A, B, C, D, E, F, G, H, I, J) -> Com_1(f5(A, B + 1, C + 1, 1, E, F, G, H, I, J)) :|: 31 >= C
3.53/1.73	f5(A, B, C, D, E, F, G, H, I, J) -> Com_1(f5(A, B, C + 1, 0, E, F, G, H, I, J)) :|: 31 >= C
3.53/1.73	f5(A, B, C, D, E, F, G, H, I, J) -> Com_1(f28(A, B, C, D, B, B, K, L, L, L)) :|: C >= 32
3.53/1.73	
3.53/1.73	The start-symbols are:[f0_10]
3.53/1.73	
3.53/1.73	
3.53/1.73	----------------------------------------
3.53/1.73	
3.53/1.73	(1) Koat Proof (FINISHED)
3.53/1.73	YES(?, 66)
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	Initial complexity problem:
3.53/1.73	
3.53/1.73	1:	T:
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f5(k, 0, 0, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9))
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f5(ar_0, ar_1 + 1, ar_2 + 1, 1, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f5(ar_0, ar_1, ar_2 + 1, 0, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f28(ar_0, ar_1, ar_2, ar_3, ar_1, ar_1, k, l, l, l)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9)) [ 0 <= 0 ]
3.53/1.73	
3.53/1.73		start location:	koat_start
3.53/1.73	
3.53/1.73		leaf cost:	0
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_2].
3.53/1.73	
3.53/1.73	We thus obtain the following problem:
3.53/1.73	
3.53/1.73	2:	T:
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f28(ar_2)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f0(ar_2) -> Com_1(f5(0))
3.53/1.73	
3.53/1.73		start location:	koat_start
3.53/1.73	
3.53/1.73		leaf cost:	0
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.53/1.73	
3.53/1.73	3:	T:
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f28(ar_2)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 1)    f0(ar_2) -> Com_1(f5(0))
3.53/1.73	
3.53/1.73		start location:	koat_start
3.53/1.73	
3.53/1.73		leaf cost:	0
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	A polynomial rank function with
3.53/1.73	
3.53/1.73		Pol(koat_start) = 1
3.53/1.73	
3.53/1.73		Pol(f0) = 1
3.53/1.73	
3.53/1.73		Pol(f5) = 1
3.53/1.73	
3.53/1.73		Pol(f28) = 0
3.53/1.73	
3.53/1.73	orients all transitions weakly and the transition
3.53/1.73	
3.53/1.73		f5(ar_2) -> Com_1(f28(ar_2)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73	strictly and produces the following problem:
3.53/1.73	
3.53/1.73	4:	T:
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 1)    f5(ar_2) -> Com_1(f28(ar_2)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 1)    f0(ar_2) -> Com_1(f5(0))
3.53/1.73	
3.53/1.73		start location:	koat_start
3.53/1.73	
3.53/1.73		leaf cost:	0
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	A polynomial rank function with
3.53/1.73	
3.53/1.73		Pol(koat_start) = 32
3.53/1.73	
3.53/1.73		Pol(f0) = 32
3.53/1.73	
3.53/1.73		Pol(f5) = -V_1 + 32
3.53/1.73	
3.53/1.73		Pol(f28) = -V_1
3.53/1.73	
3.53/1.73	orients all transitions weakly and the transition
3.53/1.73	
3.53/1.73		f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73	strictly and produces the following problem:
3.53/1.73	
3.53/1.73	5:	T:
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 0)     koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 1)     f5(ar_2) -> Com_1(f28(ar_2)) [ ar_2 >= 32 ]
3.53/1.73	
3.53/1.73			(Comp: 32, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: 32, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 31 >= ar_2 ]
3.53/1.73	
3.53/1.73			(Comp: 1, Cost: 1)     f0(ar_2) -> Com_1(f5(0))
3.53/1.73	
3.53/1.73		start location:	koat_start
3.53/1.73	
3.53/1.73		leaf cost:	0
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	Complexity upper bound 66
3.53/1.73	
3.53/1.73	
3.53/1.73	
3.53/1.73	Time: 0.065 sec (SMT: 0.061 sec)
3.53/1.73	
3.53/1.73	
3.53/1.73	----------------------------------------
3.53/1.73	
3.53/1.73	(2)
3.53/1.73	BOUNDS(1, 1)
3.67/1.75	EOF