5.63/2.59	WORST_CASE(Omega(n^2), O(n^2))
5.63/2.60	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.63/2.60	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.63/2.60	
5.63/2.60	
5.63/2.60	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.63/2.60	
5.63/2.60	(0) CpxIntTrs
5.63/2.60	(1) Koat Proof [FINISHED, 184 ms]
5.63/2.60	(2) BOUNDS(1, n^2)
5.63/2.60	(3) Loat Proof [FINISHED, 1003 ms]
5.63/2.60	(4) BOUNDS(n^2, INF)
5.63/2.60	
5.63/2.60	
5.63/2.60	----------------------------------------
5.63/2.60	
5.63/2.60	(0)
5.63/2.60	Obligation:
5.63/2.60	Complexity Int TRS consisting of the following rules:
5.63/2.60	f0(A, B, C, D, E, F, G, H) -> Com_1(f10(I, 0, C, D, E, F, G, H)) :|: TRUE
5.63/2.60	f10(A, B, C, D, E, F, G, H) -> Com_1(f10(A, B + 1, C, D, E, F, G, H)) :|: C >= B + 1
5.63/2.60	f18(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, E, E + 1, H)) :|: D >= 2 + E
5.63/2.60	f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, F, G + 1, H)) :|: D >= G + 1
5.63/2.60	f22(A, B, C, D, E, F, G, H) -> Com_1(f22(A, B, C, D, E, G, G + 1, H)) :|: D >= G + 1
5.63/2.60	f34(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, E + 1, F, G, H)) :|: D >= 2 + E
5.63/2.60	f34(A, B, C, D, E, F, G, H) -> Com_1(f43(A, B, C, D, E, F, G, H)) :|: E + 1 >= D
5.63/2.60	f22(A, B, C, D, E, F, G, H) -> Com_1(f18(A, B, C, D, E + 1, F, G, I)) :|: G >= D
5.63/2.60	f18(A, B, C, D, E, F, G, H) -> Com_1(f34(A, B, C, D, 0, F, G, H)) :|: E + 1 >= D
5.63/2.60	f10(A, B, C, D, E, F, G, H) -> Com_1(f18(A, B, C, C, 0, F, G, H)) :|: B >= C
5.63/2.60	
5.63/2.60	The start-symbols are:[f0_8]
5.63/2.60	
5.63/2.60	
5.63/2.60	----------------------------------------
5.63/2.60	
5.63/2.60	(1) Koat Proof (FINISHED)
5.63/2.60	YES(?, 44*ar_2 + 24*ar_2^2 + 10)
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	Initial complexity problem:
5.63/2.60	
5.63/2.60	1:	T:
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f10(i, 0, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7))
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f10(ar_0, ar_1 + 1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_4, ar_4 + 1, ar_7)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1, ar_7)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_6, ar_6 + 1, ar_7)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, ar_7)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f43(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f18(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, ar_5, ar_6, i)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f34(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6, ar_7)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f18(ar_0, ar_1, ar_2, ar_2, 0, ar_5, ar_6, ar_7)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_1, ar_2, ar_3, ar_4, ar_6].
5.63/2.60	
5.63/2.60	We thus obtain the following problem:
5.63/2.60	
5.63/2.60	2:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	Repeatedly propagating knowledge in problem 2 produces the following problem:
5.63/2.60	
5.63/2.60	3:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)    f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(koat_start) = 3
5.63/2.60	
5.63/2.60		Pol(f0) = 3
5.63/2.60	
5.63/2.60		Pol(f10) = 3
5.63/2.60	
5.63/2.60		Pol(f18) = 2
5.63/2.60	
5.63/2.60		Pol(f34) = 1
5.63/2.60	
5.63/2.60		Pol(f22) = 2
5.63/2.60	
5.63/2.60		Pol(f43) = 0
5.63/2.60	
5.63/2.60	orients all transitions weakly and the transitions
5.63/2.60	
5.63/2.60		f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60		f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60		f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60	strictly and produces the following problem:
5.63/2.60	
5.63/2.60	4:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)    koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)    f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(koat_start) = V_2
5.63/2.60	
5.63/2.60		Pol(f0) = V_2
5.63/2.60	
5.63/2.60		Pol(f10) = V_2
5.63/2.60	
5.63/2.60		Pol(f18) = V_3
5.63/2.60	
5.63/2.60		Pol(f34) = V_3 - V_4
5.63/2.60	
5.63/2.60		Pol(f22) = V_3
5.63/2.60	
5.63/2.60		Pol(f43) = V_3 - V_4
5.63/2.60	
5.63/2.60	orients all transitions weakly and the transition
5.63/2.60	
5.63/2.60		f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60	strictly and produces the following problem:
5.63/2.60	
5.63/2.60	5:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)       koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)       f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(koat_start) = V_2
5.63/2.60	
5.63/2.60		Pol(f0) = V_2
5.63/2.60	
5.63/2.60		Pol(f10) = -V_1 + V_2
5.63/2.60	
5.63/2.60		Pol(f18) = -V_1 + V_2
5.63/2.60	
5.63/2.60		Pol(f34) = -V_1 + V_2
5.63/2.60	
5.63/2.60		Pol(f22) = -V_1 + V_2
5.63/2.60	
5.63/2.60		Pol(f43) = -V_1 + V_2
5.63/2.60	
5.63/2.60	orients all transitions weakly and the transition
5.63/2.60	
5.63/2.60		f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60	strictly and produces the following problem:
5.63/2.60	
5.63/2.60	6:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)       koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)       f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)    f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)       f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)    f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)       f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(f22) = V_3 - V_4 - 1
5.63/2.60	
5.63/2.60		Pol(f18) = V_3 - V_4
5.63/2.60	
5.63/2.60	and size complexities
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-0) = 0
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = 0
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-3) = 0
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-0) = ar_1
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60	orients the transitions
5.63/2.60	
5.63/2.60		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60		f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60	weakly and the transition
5.63/2.60	
5.63/2.60		f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60	strictly and produces the following problem:
5.63/2.60	
5.63/2.60	7:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)         koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)         f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)      f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)         f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)         f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 3*ar_2, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)      f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)         f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(f22) = 1
5.63/2.60	
5.63/2.60		Pol(f18) = 0
5.63/2.60	
5.63/2.60	and size complexities
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-0) = 0
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-3) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = 0
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-3) = 0
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-0) = ar_1
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60	orients the transitions
5.63/2.60	
5.63/2.60		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60	weakly and the transition
5.63/2.60	
5.63/2.60		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60	strictly and produces the following problem:
5.63/2.60	
5.63/2.60	8:	T:
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 0)         koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3*ar_2, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: 3, Cost: 1)         f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)      f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)         f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: ?, Cost: 1)         f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 3*ar_2, Cost: 1)    f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.60	
5.63/2.60			(Comp: ar_2, Cost: 1)      f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.60	
5.63/2.60			(Comp: 1, Cost: 1)         f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.60	
5.63/2.60		start location:	koat_start
5.63/2.60	
5.63/2.60		leaf cost:	0
5.63/2.60	
5.63/2.60	
5.63/2.60	
5.63/2.60	A polynomial rank function with
5.63/2.60	
5.63/2.60		Pol(f22) = V_3 - V_5
5.63/2.60	
5.63/2.60	and size complexities
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-0) = 0
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-2) = ar_3
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-3) = ar_4
5.63/2.60	
5.63/2.60		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]", 0-4) = ar_6
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-3) = 3*ar_2
5.63/2.60	
5.63/2.60		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]", 0-4) = 3*ar_2 + 6
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = 3*ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-3) = 3*ar_2
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = ar_2
5.63/2.60	
5.63/2.60		S("f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.60	
5.63/2.60		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-0) = ar_2
5.63/2.61	
5.63/2.61		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-1) = ar_2
5.63/2.61	
5.63/2.61		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-2) = ar_2
5.63/2.61	
5.63/2.61		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-3) = 3*ar_2
5.63/2.61	
5.63/2.61		S("f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]", 0-4) = ?
5.63/2.61	
5.63/2.61		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-0) = ar_2
5.63/2.61	
5.63/2.61		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-1) = ar_2
5.63/2.61	
5.63/2.61		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-2) = ar_2
5.63/2.61	
5.63/2.61		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-3) = 0
5.63/2.61	
5.63/2.61		S("f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]", 0-4) = ?
5.63/2.61	
5.63/2.61		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-0) = ar_2
5.63/2.61	
5.63/2.61		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-1) = ar_2
5.63/2.61	
5.63/2.61		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-2) = ar_2
5.63/2.61	
5.63/2.61		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-3) = 0
5.63/2.61	
5.63/2.61		S("f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]", 0-4) = ar_6
5.63/2.61	
5.63/2.61		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-0) = ar_1
5.63/2.61	
5.63/2.61		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-1) = ar_2
5.63/2.61	
5.63/2.61		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-2) = ar_3
5.63/2.61	
5.63/2.61		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-3) = ar_4
5.63/2.61	
5.63/2.61		S("koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]", 0-4) = ar_6
5.63/2.61	
5.63/2.61	orients the transitions
5.63/2.61	
5.63/2.61		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.61	
5.63/2.61	weakly and the transition
5.63/2.61	
5.63/2.61		f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.61	
5.63/2.61	strictly and produces the following problem:
5.63/2.61	
5.63/2.61	9:	T:
5.63/2.61	
5.63/2.61			(Comp: 1, Cost: 0)                      koat_start(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f0(ar_1, ar_2, ar_3, ar_4, ar_6)) [ 0 <= 0 ]
5.63/2.61	
5.63/2.61			(Comp: 3, Cost: 1)                      f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_2, 0, ar_6)) [ ar_1 >= ar_2 ]
5.63/2.61	
5.63/2.61			(Comp: 3, Cost: 1)                      f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, 0, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.61	
5.63/2.61			(Comp: 3*ar_2, Cost: 1)                 f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f18(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_6 >= ar_3 ]
5.63/2.61	
5.63/2.61			(Comp: 3, Cost: 1)                      f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f43(ar_1, ar_2, ar_3, ar_4, ar_6)) [ ar_4 + 1 >= ar_3 ]
5.63/2.61	
5.63/2.61			(Comp: ar_2, Cost: 1)                   f34(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f34(ar_1, ar_2, ar_3, ar_4 + 1, ar_6)) [ ar_3 >= ar_4 + 2 ]
5.63/2.61	
5.63/2.61			(Comp: 12*ar_2^2 + 18*ar_2, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.61	
5.63/2.61			(Comp: 12*ar_2^2 + 18*ar_2, Cost: 1)    f22(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_6 + 1)) [ ar_3 >= ar_6 + 1 ]
5.63/2.61	
5.63/2.61			(Comp: 3*ar_2, Cost: 1)                 f18(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f22(ar_1, ar_2, ar_3, ar_4, ar_4 + 1)) [ ar_3 >= ar_4 + 2 ]
5.63/2.61	
5.63/2.61			(Comp: ar_2, Cost: 1)                   f10(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(ar_1 + 1, ar_2, ar_3, ar_4, ar_6)) [ ar_2 >= ar_1 + 1 ]
5.63/2.61	
5.63/2.61			(Comp: 1, Cost: 1)                      f0(ar_1, ar_2, ar_3, ar_4, ar_6) -> Com_1(f10(0, ar_2, ar_3, ar_4, ar_6))
5.63/2.61	
5.63/2.61		start location:	koat_start
5.63/2.61	
5.63/2.61		leaf cost:	0
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Complexity upper bound 44*ar_2 + 24*ar_2^2 + 10
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Time: 0.213 sec (SMT: 0.165 sec)
5.63/2.61	
5.63/2.61	
5.63/2.61	----------------------------------------
5.63/2.61	
5.63/2.61	(2)
5.63/2.61	BOUNDS(1, n^2)
5.63/2.61	
5.63/2.61	----------------------------------------
5.63/2.61	
5.63/2.61	(3) Loat Proof (FINISHED)
5.63/2.61	
5.63/2.61	
5.63/2.61	### Pre-processing the ITS problem ###
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Initial linear ITS problem
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	      0: f0 -> f10 : A'=free, B'=0, [], cost: 1
5.63/2.61	
5.63/2.61	      1: f10 -> f10 : B'=1+B, [ C>=1+B ], cost: 1
5.63/2.61	
5.63/2.61	      9: f10 -> f18 : D'=C, E'=0, [ B>=C ], cost: 1
5.63/2.61	
5.63/2.61	      2: f18 -> f22 : F'=E, G'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	      8: f18 -> f34 : E'=0, [ 1+E>=D ], cost: 1
5.63/2.61	
5.63/2.61	      3: f22 -> f22 : G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	      4: f22 -> f22 : F'=G, G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	      7: f22 -> f18 : E'=1+E, H'=free_1, [ G>=D ], cost: 1
5.63/2.61	
5.63/2.61	      5: f34 -> f34 : E'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	      6: f34 -> f43 : [ 1+E>=D ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Removed unreachable and leaf rules:
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	      0: f0 -> f10 : A'=free, B'=0, [], cost: 1
5.63/2.61	
5.63/2.61	      1: f10 -> f10 : B'=1+B, [ C>=1+B ], cost: 1
5.63/2.61	
5.63/2.61	      9: f10 -> f18 : D'=C, E'=0, [ B>=C ], cost: 1
5.63/2.61	
5.63/2.61	      2: f18 -> f22 : F'=E, G'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	      8: f18 -> f34 : E'=0, [ 1+E>=D ], cost: 1
5.63/2.61	
5.63/2.61	      3: f22 -> f22 : G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	      4: f22 -> f22 : F'=G, G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	      7: f22 -> f18 : E'=1+E, H'=free_1, [ G>=D ], cost: 1
5.63/2.61	
5.63/2.61	      5: f34 -> f34 : E'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	### Simplification by acceleration and chaining ###
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerating simple loops of location 1.
5.63/2.61	
5.63/2.61	   Accelerating the following rules:
5.63/2.61	
5.63/2.61	      1: f10 -> f10 : B'=1+B, [ C>=1+B ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	   Accelerated rule 1 with metering function C-B, yielding the new rule 10.
5.63/2.61	
5.63/2.61	   Removing the simple loops: 1.
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerating simple loops of location 3.
5.63/2.61	
5.63/2.61	   Accelerating the following rules:
5.63/2.61	
5.63/2.61	      3: f22 -> f22 : G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	      4: f22 -> f22 : F'=G, G'=1+G, [ D>=1+G ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	   Accelerated rule 3 with metering function -G+D, yielding the new rule 11.
5.63/2.61	
5.63/2.61	   Accelerated rule 4 with metering function -G+D, yielding the new rule 12.
5.63/2.61	
5.63/2.61	   Removing the simple loops: 3 4.
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerating simple loops of location 4.
5.63/2.61	
5.63/2.61	   Accelerating the following rules:
5.63/2.61	
5.63/2.61	      5: f34 -> f34 : E'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	   Accelerated rule 5 with metering function -1+D-E, yielding the new rule 13.
5.63/2.61	
5.63/2.61	   Removing the simple loops: 5.
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerated all simple loops using metering functions (where possible):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	      0: f0 -> f10 : A'=free, B'=0, [], cost: 1
5.63/2.61	
5.63/2.61	      9: f10 -> f18 : D'=C, E'=0, [ B>=C ], cost: 1
5.63/2.61	
5.63/2.61	     10: f10 -> f10 : B'=C, [ C>=1+B ], cost: C-B
5.63/2.61	
5.63/2.61	      2: f18 -> f22 : F'=E, G'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	      8: f18 -> f34 : E'=0, [ 1+E>=D ], cost: 1
5.63/2.61	
5.63/2.61	      7: f22 -> f18 : E'=1+E, H'=free_1, [ G>=D ], cost: 1
5.63/2.61	
5.63/2.61	     11: f22 -> f22 : G'=D, [ D>=1+G ], cost: -G+D
5.63/2.61	
5.63/2.61	     12: f22 -> f22 : F'=-1+D, G'=D, [ D>=1+G ], cost: -G+D
5.63/2.61	
5.63/2.61	     13: f34 -> f34 : E'=-1+D, [ D>=2+E ], cost: -1+D-E
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Chained accelerated rules (with incoming rules):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	      0: f0 -> f10 : A'=free, B'=0, [], cost: 1
5.63/2.61	
5.63/2.61	     14: f0 -> f10 : A'=free, B'=C, [ C>=1 ], cost: 1+C
5.63/2.61	
5.63/2.61	      9: f10 -> f18 : D'=C, E'=0, [ B>=C ], cost: 1
5.63/2.61	
5.63/2.61	      2: f18 -> f22 : F'=E, G'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	      8: f18 -> f34 : E'=0, [ 1+E>=D ], cost: 1
5.63/2.61	
5.63/2.61	     15: f18 -> f22 : F'=E, G'=D, [ D>=2+E ], cost: D-E
5.63/2.61	
5.63/2.61	     16: f18 -> f22 : F'=-1+D, G'=D, [ D>=2+E ], cost: D-E
5.63/2.61	
5.63/2.61	     17: f18 -> f34 : E'=-1+D, [ 1+E>=D && D>=2 ], cost: D
5.63/2.61	
5.63/2.61	      7: f22 -> f18 : E'=1+E, H'=free_1, [ G>=D ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Removed unreachable locations (and leaf rules with constant cost):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	      0: f0 -> f10 : A'=free, B'=0, [], cost: 1
5.63/2.61	
5.63/2.61	     14: f0 -> f10 : A'=free, B'=C, [ C>=1 ], cost: 1+C
5.63/2.61	
5.63/2.61	      9: f10 -> f18 : D'=C, E'=0, [ B>=C ], cost: 1
5.63/2.61	
5.63/2.61	      2: f18 -> f22 : F'=E, G'=1+E, [ D>=2+E ], cost: 1
5.63/2.61	
5.63/2.61	     15: f18 -> f22 : F'=E, G'=D, [ D>=2+E ], cost: D-E
5.63/2.61	
5.63/2.61	     16: f18 -> f22 : F'=-1+D, G'=D, [ D>=2+E ], cost: D-E
5.63/2.61	
5.63/2.61	     17: f18 -> f34 : E'=-1+D, [ 1+E>=D && D>=2 ], cost: D
5.63/2.61	
5.63/2.61	      7: f22 -> f18 : E'=1+E, H'=free_1, [ G>=D ], cost: 1
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Eliminated locations (on tree-shaped paths):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	     18: f0 -> f18 : A'=free, B'=0, D'=C, E'=0, [ 0>=C ], cost: 2
5.63/2.61	
5.63/2.61	     19: f0 -> f18 : A'=free, B'=C, D'=C, E'=0, [ C>=1 ], cost: 2+C
5.63/2.61	
5.63/2.61	     17: f18 -> f34 : E'=-1+D, [ 1+E>=D && D>=2 ], cost: D
5.63/2.61	
5.63/2.61	     20: f18 -> f18 : E'=1+E, F'=E, G'=D, H'=free_1, [ D>=2+E ], cost: 1+D-E
5.63/2.61	
5.63/2.61	     21: f18 -> f18 : E'=1+E, F'=-1+D, G'=D, H'=free_1, [ D>=2+E ], cost: 1+D-E
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerating simple loops of location 2.
5.63/2.61	
5.63/2.61	   Accelerating the following rules:
5.63/2.61	
5.63/2.61	     20: f18 -> f18 : E'=1+E, F'=E, G'=D, H'=free_1, [ D>=2+E ], cost: 1+D-E
5.63/2.61	
5.63/2.61	     21: f18 -> f18 : E'=1+E, F'=-1+D, G'=D, H'=free_1, [ D>=2+E ], cost: 1+D-E
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	   Accelerated rule 20 with metering function -1+D-E, yielding the new rule 22.
5.63/2.61	
5.63/2.61	   Accelerated rule 21 with metering function -1+D-E, yielding the new rule 23.
5.63/2.61	
5.63/2.61	   Removing the simple loops: 20 21.
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Accelerated all simple loops using metering functions (where possible):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	     18: f0 -> f18 : A'=free, B'=0, D'=C, E'=0, [ 0>=C ], cost: 2
5.63/2.61	
5.63/2.61	     19: f0 -> f18 : A'=free, B'=C, D'=C, E'=0, [ C>=1 ], cost: 2+C
5.63/2.61	
5.63/2.61	     17: f18 -> f34 : E'=-1+D, [ 1+E>=D && D>=2 ], cost: D
5.63/2.61	
5.63/2.61	     22: f18 -> f18 : E'=-1+D, F'=-2+D, G'=D, H'=free_1, [ D>=2+E ], cost: -3/2-1/2*(-1+D-E)^2-(-1+D-E)*E+D*(-1+D-E)+3/2*D-3/2*E
5.63/2.61	
5.63/2.61	     23: f18 -> f18 : E'=-1+D, F'=-1+D, G'=D, H'=free_1, [ D>=2+E ], cost: -3/2-1/2*(-1+D-E)^2-(-1+D-E)*E+D*(-1+D-E)+3/2*D-3/2*E
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Chained accelerated rules (with incoming rules):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	     18: f0 -> f18 : A'=free, B'=0, D'=C, E'=0, [ 0>=C ], cost: 2
5.63/2.61	
5.63/2.61	     19: f0 -> f18 : A'=free, B'=C, D'=C, E'=0, [ C>=1 ], cost: 2+C
5.63/2.61	
5.63/2.61	     24: f0 -> f18 : A'=free, B'=C, D'=C, E'=-1+C, F'=-2+C, G'=C, H'=free_1, [ C>=2 ], cost: 1/2+5/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	     25: f0 -> f18 : A'=free, B'=C, D'=C, E'=-1+C, F'=-1+C, G'=C, H'=free_1, [ C>=2 ], cost: 1/2+5/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	     17: f18 -> f34 : E'=-1+D, [ 1+E>=D && D>=2 ], cost: D
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Eliminated locations (on tree-shaped paths):
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	     26: f0 -> f34 : A'=free, B'=C, D'=C, E'=-1+C, F'=-2+C, G'=C, H'=free_1, [ C>=2 ], cost: 1/2+7/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	     27: f0 -> f34 : A'=free, B'=C, D'=C, E'=-1+C, F'=-1+C, G'=C, H'=free_1, [ C>=2 ], cost: 1/2+7/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	     28: f0 -> [10] : [ C>=1 ], cost: 2+C
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	### Computing asymptotic complexity ###
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Fully simplified ITS problem
5.63/2.61	
5.63/2.61	   Start location: f0
5.63/2.61	
5.63/2.61	     27: f0 -> f34 : A'=free, B'=C, D'=C, E'=-1+C, F'=-1+C, G'=C, H'=free_1, [ C>=2 ], cost: 1/2+7/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	     28: f0 -> [10] : [ C>=1 ], cost: 2+C
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Computing asymptotic complexity for rule 27
5.63/2.61	
5.63/2.61	   Solved the limit problem by the following transformations:
5.63/2.61	
5.63/2.61	      Created initial limit problem:
5.63/2.61	
5.63/2.61	      1/2*C^2+7/2*C (+), -1+C (+/+!) [not solved]
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	      removing all constraints (solved by SMT)
5.63/2.61	
5.63/2.61	      resulting limit problem: [solved]
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	      applying transformation rule (C) using substitution {C==n}
5.63/2.61	
5.63/2.61	      resulting limit problem:
5.63/2.61	
5.63/2.61	      [solved]
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	   Solution:
5.63/2.61	
5.63/2.61	      C / n
5.63/2.61	
5.63/2.61	   Resulting cost 7/2*n+1/2*n^2 has complexity: Poly(n^2)
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Found new complexity Poly(n^2).
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	Obtained the following overall complexity (w.r.t. the length of the input n):
5.63/2.61	
5.63/2.61	   Complexity:  Poly(n^2)
5.63/2.61	
5.63/2.61	   Cpx degree:  2
5.63/2.61	
5.63/2.61	   Solved cost: 7/2*n+1/2*n^2
5.63/2.61	
5.63/2.61	   Rule cost:   1/2+7/2*C+C*(-1+C)-1/2*(-1+C)^2
5.63/2.61	
5.63/2.61	   Rule guard:  [ C>=2 ]
5.63/2.61	
5.63/2.61	
5.63/2.61	
5.63/2.61	WORST_CASE(Omega(n^2),?)
5.63/2.61	
5.63/2.61	
5.63/2.61	----------------------------------------
5.63/2.61	
5.63/2.61	(4)
5.63/2.61	BOUNDS(n^2, INF)
5.63/2.63	EOF