3.57/1.78	WORST_CASE(?, O(1))
3.57/1.78	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.57/1.78	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.57/1.78	
3.57/1.78	
3.57/1.78	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.57/1.78	
3.57/1.78	(0) CpxIntTrs
3.57/1.78	(1) Koat Proof [FINISHED, 110 ms]
3.57/1.78	(2) BOUNDS(1, 1)
3.57/1.78	
3.57/1.78	
3.57/1.78	----------------------------------------
3.57/1.78	
3.57/1.78	(0)
3.57/1.78	Obligation:
3.57/1.78	Complexity Int TRS consisting of the following rules:
3.57/1.78	f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f6(0, 0, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: TRUE
3.57/1.78	f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f6(U, B + 1, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: 63 >= B
3.57/1.78	f14(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f14(A, B, C - 1, U + V, W, X + Y, Z, A1 + B1, C1, D1 + E1, F1, U + V + D1 + E1, U + V - D1 - E1, X + Y + A1 + B1, X + Y - A1 - B1, G1, H1, I1 + J1, K1 + J1, J1)) :|: C >= 0
3.57/1.78	f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f57(A, B, C - 1, U + V, W, X + Y, Z, A1 + B1, C1, D1 + E1, F1, U + V + D1 + E1, U + V - D1 - E1, X + Y + A1 + B1, X + Y - A1 - B1, G1, H1, I1 + J1, K1 + J1, J1)) :|: C >= 0
3.57/1.78	f57(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f101(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: 0 >= C + 1
3.57/1.78	f14(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f57(A, B, 7, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: 0 >= C + 1
3.57/1.78	f6(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T) -> Com_1(f14(A, B, 7, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T)) :|: B >= 64
3.57/1.78	
3.57/1.78	The start-symbols are:[f0_20]
3.57/1.78	
3.57/1.78	
3.57/1.78	----------------------------------------
3.57/1.78	
3.57/1.78	(1) Koat Proof (FINISHED)
3.57/1.78	YES(?, 106)
3.57/1.78	
3.57/1.78	
3.57/1.78	
3.57/1.78	Initial complexity problem:
3.57/1.78	
3.57/1.78	1:	T:
3.57/1.78	
3.57/1.78			(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) -> Com_1(f6(0, 0, 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))
3.57/1.78	
3.57/1.78			(Comp: ?, Cost: 1)    f6(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) -> Com_1(f6(u, ar_1 + 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)) [ 63 >= ar_1 ]
3.57/1.78	
3.57/1.78			(Comp: ?, Cost: 1)    f14(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) -> Com_1(f14(ar_0, ar_1, ar_2 - 1, u + v, w, x + y, z, a1 + b1, c1, d1 + e1, f1, u + v + d1 + e1, u + v - d1 - e1, x + y + a1 + b1, x + y - a1 - b1, g1, h1, i1 + j1, k1 + j1, j1)) [ ar_2 >= 0 ]
3.57/1.78	
3.57/1.78			(Comp: ?, Cost: 1)    f57(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) -> Com_1(f57(ar_0, ar_1, ar_2 - 1, u + v, w, x + y, z, a1 + b1, c1, d1 + e1, f1, u + v + d1 + e1, u + v - d1 - e1, x + y + a1 + b1, x + y - a1 - b1, g1, h1, i1 + j1, k1 + j1, j1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(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) -> Com_1(f101(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)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(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) -> Com_1(f57(ar_0, ar_1, 7, 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)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(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) -> Com_1(f14(ar_0, ar_1, 7, 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_1 >= 64 ]
3.57/1.79	
3.57/1.79			(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) -> 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)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_1, ar_2].
3.57/1.79	
3.57/1.79	We thus obtain the following problem:
3.57/1.79	
3.57/1.79	2:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.57/1.79	
3.57/1.79	3:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 1)    f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	A polynomial rank function with
3.57/1.79	
3.57/1.79		Pol(koat_start) = 3
3.57/1.79	
3.57/1.79		Pol(f0) = 3
3.57/1.79	
3.57/1.79		Pol(f6) = 3
3.57/1.79	
3.57/1.79		Pol(f14) = 2
3.57/1.79	
3.57/1.79		Pol(f57) = 1
3.57/1.79	
3.57/1.79		Pol(f101) = 0
3.57/1.79	
3.57/1.79	orients all transitions weakly and the transitions
3.57/1.79	
3.57/1.79		f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79		f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79		f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79	strictly and produces the following problem:
3.57/1.79	
3.57/1.79	4:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 1)    f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	A polynomial rank function with
3.57/1.79	
3.57/1.79		Pol(koat_start) = 8
3.57/1.79	
3.57/1.79		Pol(f0) = 8
3.57/1.79	
3.57/1.79		Pol(f6) = 8
3.57/1.79	
3.57/1.79		Pol(f14) = 8
3.57/1.79	
3.57/1.79		Pol(f57) = V_2 + 1
3.57/1.79	
3.57/1.79		Pol(f101) = V_2
3.57/1.79	
3.57/1.79	orients all transitions weakly and the transition
3.57/1.79	
3.57/1.79		f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79	strictly and produces the following problem:
3.57/1.79	
3.57/1.79	5:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 8, Cost: 1)    f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 1)    f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	A polynomial rank function with
3.57/1.79	
3.57/1.79		Pol(koat_start) = 64
3.57/1.79	
3.57/1.79		Pol(f0) = 64
3.57/1.79	
3.57/1.79		Pol(f6) = -V_1 + 64
3.57/1.79	
3.57/1.79		Pol(f14) = -V_1
3.57/1.79	
3.57/1.79		Pol(f57) = -V_1
3.57/1.79	
3.57/1.79		Pol(f101) = -V_1
3.57/1.79	
3.57/1.79	orients all transitions weakly and the transition
3.57/1.79	
3.57/1.79		f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79	strictly and produces the following problem:
3.57/1.79	
3.57/1.79	6:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)     koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 8, Cost: 1)     f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: ?, Cost: 1)     f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 64, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 1)     f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	A polynomial rank function with
3.57/1.79	
3.57/1.79		Pol(f14) = V_2 + 1
3.57/1.79	
3.57/1.79	and size complexities
3.57/1.79	
3.57/1.79		S("f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))", 0-0) = 0
3.57/1.79	
3.57/1.79		S("f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))", 0-1) = ar_2
3.57/1.79	
3.57/1.79		S("f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]", 0-1) = ar_2
3.57/1.79	
3.57/1.79		S("f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]", 0-1) = 7
3.57/1.79	
3.57/1.79		S("f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]", 0-1) = 7
3.57/1.79	
3.57/1.79		S("f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]", 0-1) = 7
3.57/1.79	
3.57/1.79		S("f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]", 0-1) = 7
3.57/1.79	
3.57/1.79		S("f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]", 0-0) = 64
3.57/1.79	
3.57/1.79		S("f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]", 0-1) = 7
3.57/1.79	
3.57/1.79		S("koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_1
3.57/1.79	
3.57/1.79		S("koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_2
3.57/1.79	
3.57/1.79	orients the transitions
3.57/1.79	
3.57/1.79		f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79	weakly and the transition
3.57/1.79	
3.57/1.79		f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79	strictly and produces the following problem:
3.57/1.79	
3.57/1.79	7:	T:
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 0)     koat_start(ar_1, ar_2) -> Com_1(f0(ar_1, ar_2)) [ 0 <= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f6(ar_1, ar_2) -> Com_1(f14(ar_1, 7)) [ ar_1 >= 64 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f14(ar_1, ar_2) -> Com_1(f57(ar_1, 7)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 3, Cost: 1)     f57(ar_1, ar_2) -> Com_1(f101(ar_1, ar_2)) [ 0 >= ar_2 + 1 ]
3.57/1.79	
3.57/1.79			(Comp: 8, Cost: 1)     f57(ar_1, ar_2) -> Com_1(f57(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 24, Cost: 1)    f14(ar_1, ar_2) -> Com_1(f14(ar_1, ar_2 - 1)) [ ar_2 >= 0 ]
3.57/1.79	
3.57/1.79			(Comp: 64, Cost: 1)    f6(ar_1, ar_2) -> Com_1(f6(ar_1 + 1, ar_2)) [ 63 >= ar_1 ]
3.57/1.79	
3.57/1.79			(Comp: 1, Cost: 1)     f0(ar_1, ar_2) -> Com_1(f6(0, ar_2))
3.57/1.79	
3.57/1.79		start location:	koat_start
3.57/1.79	
3.57/1.79		leaf cost:	0
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	Complexity upper bound 106
3.57/1.79	
3.57/1.79	
3.57/1.79	
3.57/1.79	Time: 0.109 sec (SMT: 0.100 sec)
3.57/1.79	
3.57/1.79	
3.57/1.79	----------------------------------------
3.57/1.79	
3.57/1.79	(2)
3.57/1.79	BOUNDS(1, 1)
3.87/1.80	EOF