3.43/1.70	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3.64/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 44 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, D, E, F, G, H, I, J) -> Com_1(f5(K, 0, 0, D, E, F, G, H, I, J)) :|: TRUE
3.64/1.71	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)) :|: 15 >= C
3.64/1.71	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)) :|: 15 >= C
3.64/1.71	f5(A, B, C, D, E, F, G, H, I, J) -> Com_1(f27(A, B, C, D, B, B, K, L, L, L)) :|: C >= 16
3.64/1.71	
3.64/1.71	The start-symbols are:[f0_10]
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(?, 34)
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, 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))
3.64/1.71	
3.64/1.71			(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)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(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)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(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(f27(ar_0, ar_1, ar_2, ar_3, ar_1, ar_1, k, l, l, l)) [ ar_2 >= 16 ]
3.64/1.71	
3.64/1.71			(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 ]
3.64/1.71	
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	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_2].
3.64/1.71	
3.64/1.71	We thus obtain the following problem:
3.64/1.71	
3.64/1.71	2:	T:
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f27(ar_2)) [ ar_2 >= 16 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f0(ar_2) -> Com_1(f5(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 2 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: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f27(ar_2)) [ ar_2 >= 16 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)    f0(ar_2) -> Com_1(f5(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(koat_start) = 1
3.64/1.71	
3.64/1.71		Pol(f0) = 1
3.64/1.71	
3.64/1.71		Pol(f5) = 1
3.64/1.71	
3.64/1.71		Pol(f27) = 0
3.64/1.71	
3.64/1.71	orients all transitions weakly and the transition
3.64/1.71	
3.64/1.71		f5(ar_2) -> Com_1(f27(ar_2)) [ ar_2 >= 16 ]
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: 0)    koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)    f5(ar_2) -> Com_1(f27(ar_2)) [ ar_2 >= 16 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: ?, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)    f0(ar_2) -> Com_1(f5(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(koat_start) = 16
3.64/1.71	
3.64/1.71		Pol(f0) = 16
3.64/1.71	
3.64/1.71		Pol(f5) = -V_1 + 16
3.64/1.71	
3.64/1.71		Pol(f27) = -V_1
3.64/1.71	
3.64/1.71	orients all transitions weakly and the transition
3.64/1.71	
3.64/1.71		f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
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: 0)     koat_start(ar_2) -> Com_1(f0(ar_2)) [ 0 <= 0 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)     f5(ar_2) -> Com_1(f27(ar_2)) [ ar_2 >= 16 ]
3.64/1.71	
3.64/1.71			(Comp: 16, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: 16, Cost: 1)    f5(ar_2) -> Com_1(f5(ar_2 + 1)) [ 15 >= ar_2 ]
3.64/1.71	
3.64/1.71			(Comp: 1, Cost: 1)     f0(ar_2) -> Com_1(f5(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 34
3.64/1.71	
3.64/1.71	
3.64/1.71	
3.64/1.71	Time: 0.066 sec (SMT: 0.064 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)
3.66/2.65	EOF