3.82/1.78	WORST_CASE(?, O(1))
4.02/1.79	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.02/1.79	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.02/1.79	
4.02/1.79	
4.02/1.79	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
4.02/1.79	
4.02/1.79	(0) CpxIntTrs
4.02/1.79	(1) Koat Proof [FINISHED, 102 ms]
4.02/1.79	(2) BOUNDS(1, 1)
4.02/1.79	
4.02/1.79	
4.02/1.79	----------------------------------------
4.02/1.79	
4.02/1.79	(0)
4.02/1.79	Obligation:
4.02/1.79	Complexity Int TRS consisting of the following rules:
4.02/1.79	f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f12(3, T, 3, 1, 0, F, G, H, I, J, K, L, M, N, O, P, Q, R, S)) :|: TRUE
4.02/1.79	f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f12(A, B, C, T, E + 1, F, G, H, I, J, K, L, M, N, O, P, Q, R, S)) :|: C >= E + 1
4.02/1.79	f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f24(A, B, C, D, E, F, G + 1, T, I, J, K, L, M, N, O, P, Q, R, S)) :|: F >= G + 1
4.02/1.79	f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f36(A, B, C, D, E, F, G, H, I, J + 1, T, L, M, N, O, P, Q, R, S)) :|: I >= J + 1
4.02/1.79	f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f46(A, B, C, D, E, F, G, H, I, J, K, K, K, N, O, P, Q, R, S)) :|: J >= I
4.02/1.79	f24(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f36(A, B, C, D, E, F, G, H, A, 0, 1, L, M, H, H, T, Q, R, S)) :|: G >= F
4.02/1.79	f12(A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S) -> Com_1(f24(A, B, C, D, E, A, 0, 1, I, J, K, L, M, N, O, P, D, D, T)) :|: E >= C
4.02/1.79	
4.02/1.79	The start-symbols are:[f0_19]
4.02/1.79	
4.02/1.79	
4.02/1.79	----------------------------------------
4.02/1.79	
4.02/1.79	(1) Koat Proof (FINISHED)
4.02/1.79	YES(?, 19)
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	Initial complexity problem:
4.02/1.79	
4.02/1.79	1:	T:
4.02/1.79	
4.02/1.79			(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) -> Com_1(f12(3, t, 3, 1, 0, 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))
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(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) -> Com_1(f12(ar_0, ar_1, ar_2, t, ar_4 + 1, 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_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(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) -> Com_1(f24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, t, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(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) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9 + 1, t, ar_11, ar_12, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(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) -> Com_1(f46(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_8, ar_9, ar_10, ar_10, ar_10, ar_13, ar_14, ar_15, ar_16, ar_17, ar_18)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(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) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7, ar_0, 0, 1, ar_11, ar_12, ar_7, ar_7, t, ar_16, ar_17, ar_18)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(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) -> Com_1(f24(ar_0, ar_1, ar_2, ar_3, ar_4, ar_0, 0, 1, ar_8, ar_9, ar_10, ar_11, ar_12, ar_13, ar_14, ar_15, ar_3, ar_3, t)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(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) -> 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)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9].
4.02/1.79	
4.02/1.79	We thus obtain the following problem:
4.02/1.79	
4.02/1.79	2:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	Repeatedly propagating knowledge in problem 2 produces the following problem:
4.02/1.79	
4.02/1.79	3:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	A polynomial rank function with
4.02/1.79	
4.02/1.79		Pol(koat_start) = 3
4.02/1.79	
4.02/1.79		Pol(f0) = 3
4.02/1.79	
4.02/1.79		Pol(f12) = 3
4.02/1.79	
4.02/1.79		Pol(f24) = 2
4.02/1.79	
4.02/1.79		Pol(f36) = 1
4.02/1.79	
4.02/1.79		Pol(f46) = 0
4.02/1.79	
4.02/1.79	orients all transitions weakly and the transitions
4.02/1.79	
4.02/1.79		f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79		f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79		f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79	strictly and produces the following problem:
4.02/1.79	
4.02/1.79	4:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	A polynomial rank function with
4.02/1.79	
4.02/1.79		Pol(koat_start) = 3
4.02/1.79	
4.02/1.79		Pol(f0) = 3
4.02/1.79	
4.02/1.79		Pol(f12) = V_1
4.02/1.79	
4.02/1.79		Pol(f24) = V_1
4.02/1.79	
4.02/1.79		Pol(f36) = V_6 - V_7
4.02/1.79	
4.02/1.79		Pol(f46) = V_6 - V_7
4.02/1.79	
4.02/1.79	orients all transitions weakly and the transition
4.02/1.79	
4.02/1.79		f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79	strictly and produces the following problem:
4.02/1.79	
4.02/1.79	5:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	A polynomial rank function with
4.02/1.79	
4.02/1.79		Pol(koat_start) = 3
4.02/1.79	
4.02/1.79		Pol(f0) = 3
4.02/1.79	
4.02/1.79		Pol(f12) = V_1
4.02/1.79	
4.02/1.79		Pol(f24) = V_4 - V_5
4.02/1.79	
4.02/1.79		Pol(f36) = V_4 - V_5
4.02/1.79	
4.02/1.79		Pol(f46) = V_4 - V_5
4.02/1.79	
4.02/1.79	orients all transitions weakly and the transition
4.02/1.79	
4.02/1.79		f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79	strictly and produces the following problem:
4.02/1.79	
4.02/1.79	6:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: ?, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	A polynomial rank function with
4.02/1.79	
4.02/1.79		Pol(koat_start) = 3
4.02/1.79	
4.02/1.79		Pol(f0) = 3
4.02/1.79	
4.02/1.79		Pol(f12) = V_2 - V_3
4.02/1.79	
4.02/1.79		Pol(f24) = V_2 - V_3
4.02/1.79	
4.02/1.79		Pol(f36) = V_2 - V_3
4.02/1.79	
4.02/1.79		Pol(f46) = V_2 - V_3
4.02/1.79	
4.02/1.79	orients all transitions weakly and the transition
4.02/1.79	
4.02/1.79		f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79	strictly and produces the following problem:
4.02/1.79	
4.02/1.79	7:	T:
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ 0 <= 0 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_0, 0, ar_8, ar_9)) [ ar_4 >= ar_2 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_0, 0)) [ ar_6 >= ar_5 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f46(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9)) [ ar_9 >= ar_8 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f36(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9 + 1)) [ ar_8 >= ar_9 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f24(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f24(ar_0, ar_2, ar_4, ar_5, ar_6 + 1, ar_8, ar_9)) [ ar_5 >= ar_6 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 3, Cost: 1)    f12(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(ar_0, ar_2, ar_4 + 1, ar_5, ar_6, ar_8, ar_9)) [ ar_2 >= ar_4 + 1 ]
4.02/1.79	
4.02/1.79			(Comp: 1, Cost: 1)    f0(ar_0, ar_2, ar_4, ar_5, ar_6, ar_8, ar_9) -> Com_1(f12(3, 3, 0, ar_5, ar_6, ar_8, ar_9))
4.02/1.79	
4.02/1.79		start location:	koat_start
4.02/1.79	
4.02/1.79		leaf cost:	0
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	Complexity upper bound 19
4.02/1.79	
4.02/1.79	
4.02/1.79	
4.02/1.79	Time: 0.157 sec (SMT: 0.127 sec)
4.02/1.79	
4.02/1.79	
4.02/1.79	----------------------------------------
4.02/1.79	
4.02/1.79	(2)
4.02/1.79	BOUNDS(1, 1)
4.04/1.81	EOF