3.34/1.62	WORST_CASE(?, O(1))
3.34/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.34/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.34/1.62	
3.34/1.62	
3.34/1.62	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.34/1.62	
3.34/1.62	(0) CpxIntTrs
3.34/1.62	(1) Koat Proof [FINISHED, 27 ms]
3.34/1.62	(2) BOUNDS(1, 1)
3.34/1.62	
3.34/1.62	
3.34/1.62	----------------------------------------
3.34/1.62	
3.34/1.62	(0)
3.34/1.62	Obligation:
3.34/1.62	Complexity Int TRS consisting of the following rules:
3.34/1.62	f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z, A1, B1, C1, D1, E1, F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1, Q1, R1, S1, T1, U1, V1) -> Com_1(f75(2, W1, W1, W1, W1, W1, 2, X1, X1, X1, X1, X1, 2, Y1, Y1, Y1, Y1, Y1, 2, Z1, Z1, Z1, Z1, Z1, 2, A2, A2, A2, A2, A2, 2, B2, B2, B2, B2, B2, 2, C2, C2, C2, C2, C2, 2, D2, D2, D2, D2, D2)) :|: TRUE
3.34/1.62	
3.34/1.62	The start-symbols are:[f0_48]
3.34/1.62	
3.34/1.62	
3.34/1.62	----------------------------------------
3.34/1.62	
3.34/1.62	(1) Koat Proof (FINISHED)
3.34/1.62	YES(?, 1)
3.34/1.62	
3.34/1.62	
3.34/1.62	
3.34/1.62	Initial complexity problem:
3.34/1.62	
3.34/1.62	1:	T:
3.34/1.62	
3.34/1.62			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29, ar_30, ar_31, ar_32, ar_33, ar_34, ar_35, ar_36, ar_37, ar_38, ar_39, ar_40, ar_41, ar_42, ar_43, ar_44, ar_45, ar_46, ar_47) -> Com_1(f75(2, w1, w1, w1, w1, w1, 2, x1, x1, x1, x1, x1, 2, y1, y1, y1, y1, y1, 2, z1, z1, z1, z1, z1, 2, a2, a2, a2, a2, a2, 2, b2, b2, b2, b2, b2, 2, c2, c2, c2, c2, c2, 2, d2, d2, d2, d2, d2))
3.34/1.62	
3.34/1.62			(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, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29, ar_30, ar_31, ar_32, ar_33, ar_34, ar_35, ar_36, ar_37, ar_38, ar_39, ar_40, ar_41, ar_42, ar_43, ar_44, ar_45, ar_46, ar_47) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18, ar_19, ar_20, ar_21, ar_22, ar_23, ar_24, ar_25, ar_26, ar_27, ar_28, ar_29, ar_30, ar_31, ar_32, ar_33, ar_34, ar_35, ar_36, ar_37, ar_38, ar_39, ar_40, ar_41, ar_42, ar_43, ar_44, ar_45, ar_46, ar_47)) [ 0 <= 0 ]
3.34/1.62	
3.34/1.62		start location:	koat_start
3.34/1.62	
3.34/1.62		leaf cost:	0
3.34/1.62	
3.34/1.62	
3.34/1.62	
3.34/1.62	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [].
3.34/1.62	
3.34/1.62	We thus obtain the following problem:
3.34/1.62	
3.34/1.62	2:	T:
3.34/1.62	
3.34/1.62			(Comp: 1, Cost: 0)    koat_start() -> Com_1(f0()) [ 0 <= 0 ]
3.34/1.62	
3.34/1.62			(Comp: ?, Cost: 1)    f0() -> Com_1(f75())
3.34/1.62	
3.34/1.62		start location:	koat_start
3.34/1.62	
3.34/1.62		leaf cost:	0
3.34/1.62	
3.34/1.62	
3.34/1.62	
3.34/1.62	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.34/1.62	
3.34/1.62	3:	T:
3.34/1.62	
3.34/1.62			(Comp: 1, Cost: 0)    koat_start() -> Com_1(f0()) [ 0 <= 0 ]
3.34/1.62	
3.34/1.62			(Comp: 1, Cost: 1)    f0() -> Com_1(f75())
3.34/1.62	
3.34/1.62		start location:	koat_start
3.34/1.62	
3.34/1.62		leaf cost:	0
3.34/1.62	
3.34/1.62	
3.34/1.62	
3.34/1.62	Complexity upper bound 1
3.34/1.62	
3.34/1.62	
3.34/1.62	
3.34/1.62	Time: 0.002 sec (SMT: 0.002 sec)
3.34/1.62	
3.34/1.62	
3.34/1.62	----------------------------------------
3.34/1.62	
3.34/1.62	(2)
3.34/1.62	BOUNDS(1, 1)
3.34/1.65	EOF