3.93/1.91	WORST_CASE(?, O(1))
4.22/1.92	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.22/1.92	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.22/1.92	
4.22/1.92	
4.22/1.92	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
4.22/1.92	
4.22/1.92	(0) CpxIntTrs
4.22/1.92	(1) Koat Proof [FINISHED, 212 ms]
4.22/1.92	(2) BOUNDS(1, 1)
4.22/1.92	
4.22/1.92	
4.22/1.92	----------------------------------------
4.22/1.92	
4.22/1.92	(0)
4.22/1.92	Obligation:
4.22/1.92	Complexity Int TRS consisting of the following rules:
4.22/1.92	f0(A, B, C, D, E, F, G) -> Com_1(f25(5, 5, 0, 0, E, F, G)) :|: TRUE
4.22/1.92	f25(A, B, C, D, E, F, G) -> Com_1(f25(A, B, C, C + 1, E, F, G)) :|: A >= D + 1 && C >= D && C <= D
4.22/1.92	f25(A, B, C, D, E, F, G) -> Com_1(f25(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && C >= D + 1
4.22/1.92	f25(A, B, C, D, E, F, G) -> Com_1(f25(A, B, C, D + 1, E, F, G)) :|: A >= D + 1 && D >= 1 + C
4.22/1.92	f33(A, B, C, D, E, F, G) -> Com_1(f36(A, B, C, D, 0, F, G)) :|: A >= D + 1
4.22/1.92	f36(A, B, C, D, E, F, G) -> Com_1(f36(A, B, C, D, E + 1, H, I)) :|: B >= E + 1
4.22/1.92	f47(A, B, C, D, E, F, G) -> Com_1(f53(A, B, C, D, E, H, I)) :|: B >= D + 1
4.22/1.92	f47(A, B, C, D, E, F, G) -> Com_1(f47(A, B, C, D + 1, E, H, I)) :|: B >= D + 1
4.22/1.92	f57(A, B, C, D, E, F, G) -> Com_1(f57(A, B, C, D + 1, E, F, G)) :|: A >= D + 1
4.22/1.92	f57(A, B, C, D, E, F, G) -> Com_1(f53(A, B, C, D, E, F, G)) :|: D >= A
4.22/1.92	f47(A, B, C, D, E, F, G) -> Com_1(f57(A, B, C, 0, E, F, G)) :|: D >= B
4.22/1.92	f36(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, D + 1, E, F, G)) :|: E >= B
4.22/1.92	f33(A, B, C, D, E, F, G) -> Com_1(f47(A, B, C, 0, E, F, G)) :|: D >= A
4.22/1.92	f25(A, B, C, D, E, F, G) -> Com_1(f33(A, B, C, 0, E, F, G)) :|: D >= A
4.22/1.92	
4.22/1.92	The start-symbols are:[f0_7]
4.22/1.92	
4.22/1.92	
4.22/1.92	----------------------------------------
4.22/1.92	
4.22/1.92	(1) Koat Proof (FINISHED)
4.22/1.92	YES(?, 722)
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Initial complexity problem:
4.22/1.92	
4.22/1.92	1:	T:
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f25(5, 5, 0, 0, ar_4, ar_5, ar_6))
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1, h, i)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, h, i)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4, ar_5, ar_6)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0, ar_1, ar_2, ar_3, ar_4].
4.22/1.92	
4.22/1.92	We thus obtain the following problem:
4.22/1.92	
4.22/1.92	2:	T:
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Testing for reachability in the complexity graph removes the following transition from problem 2:
4.22/1.92	
4.22/1.92		f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92	We thus obtain the following problem:
4.22/1.92	
4.22/1.92	3:	T:
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Repeatedly propagating knowledge in problem 3 produces the following problem:
4.22/1.92	
4.22/1.92	4:	T:
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	A polynomial rank function with
4.22/1.92	
4.22/1.92		Pol(f57) = 1
4.22/1.92	
4.22/1.92		Pol(f53) = 0
4.22/1.92	
4.22/1.92		Pol(f36) = 3
4.22/1.92	
4.22/1.92		Pol(f33) = 3
4.22/1.92	
4.22/1.92		Pol(f47) = 2
4.22/1.92	
4.22/1.92		Pol(f25) = 4
4.22/1.92	
4.22/1.92		Pol(f0) = 4
4.22/1.92	
4.22/1.92		Pol(koat_start) = 4
4.22/1.92	
4.22/1.92	orients all transitions weakly and the transitions
4.22/1.92	
4.22/1.92		f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92		f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92		f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92		f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92	strictly and produces the following problem:
4.22/1.92	
4.22/1.92	5:	T:
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	A polynomial rank function with
4.22/1.92	
4.22/1.92		Pol(f57) = V_1 - V_4
4.22/1.92	
4.22/1.92		Pol(f47) = V_2 - V_4
4.22/1.92	
4.22/1.92		Pol(f36) = V_1 - V_4
4.22/1.92	
4.22/1.92		Pol(f33) = V_1 - V_4 + 1
4.22/1.92	
4.22/1.92		Pol(f25) = V_1 - V_4
4.22/1.92	
4.22/1.92	and size complexities
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92	orients the transitions
4.22/1.92	
4.22/1.92		f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92		f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92	weakly and the transitions
4.22/1.92	
4.22/1.92		f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92		f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92	strictly and produces the following problem:
4.22/1.92	
4.22/1.92	6:	T:
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)     f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)     f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)     f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	A polynomial rank function with
4.22/1.92	
4.22/1.92		Pol(f36) = 1
4.22/1.92	
4.22/1.92		Pol(f33) = 0
4.22/1.92	
4.22/1.92	and size complexities
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 71
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92	orients the transitions
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92	weakly and the transition
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92	strictly and produces the following problem:
4.22/1.92	
4.22/1.92	7:	T:
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: ?, Cost: 1)     f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)    f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)     f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)     f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	A polynomial rank function with
4.22/1.92	
4.22/1.92		Pol(f36) = V_2 - V_5
4.22/1.92	
4.22/1.92	and size complexities
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.22/1.92	
4.22/1.92		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-3) = 1
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_2 = ar_3 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = 71
4.22/1.92	
4.22/1.92		S("f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\\ ar_3 >= ar_2 + 1 ]", 0-4) = ar_4
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]", 0-4) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-3) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]", 0-4) = ?
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-0) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-1) = 5
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-2) = 0
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-3) = 70
4.22/1.92	
4.22/1.92		S("f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]", 0-4) = ?
4.22/1.92	
4.22/1.92	orients the transitions
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92	weakly and the transition
4.22/1.92	
4.22/1.92		f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92	strictly and produces the following problem:
4.22/1.92	
4.22/1.92	8:	T:
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)     f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)      f57(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 350, Cost: 1)    f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_1 >= ar_4 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)     f36(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)      f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f53(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)     f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_1 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)      f47(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f57(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_1 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)     f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f36(ar_0, ar_1, ar_2, ar_3, 0)) [ ar_0 >= ar_3 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)      f33(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f47(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 70, Cost: 1)     f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_3 >= ar_2 + 1 ]
4.22/1.92	
4.22/1.92			(Comp: 4, Cost: 1)      f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f33(ar_0, ar_1, ar_2, 0, ar_4)) [ ar_3 >= ar_0 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)      f25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(ar_0, ar_1, ar_2, ar_2 + 1, ar_4)) [ ar_0 >= ar_3 + 1 /\ ar_2 = ar_3 ]
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f25(5, 5, 0, 0, ar_4))
4.22/1.92	
4.22/1.92			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f0(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.22/1.92	
4.22/1.92		start location:	koat_start
4.22/1.92	
4.22/1.92		leaf cost:	0
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Complexity upper bound 722
4.22/1.92	
4.22/1.92	
4.22/1.92	
4.22/1.92	Time: 0.233 sec (SMT: 0.192 sec)
4.22/1.92	
4.22/1.92	
4.22/1.92	----------------------------------------
4.22/1.92	
4.22/1.92	(2)
4.22/1.92	BOUNDS(1, 1)
4.22/1.93	EOF