4.08/1.98	WORST_CASE(?, O(1))
4.08/1.99	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.08/1.99	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.08/1.99	
4.08/1.99	
4.08/1.99	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
4.08/1.99	
4.08/1.99	(0) CpxIntTrs
4.08/1.99	(1) Koat Proof [FINISHED, 216 ms]
4.08/1.99	(2) BOUNDS(1, 1)
4.08/1.99	
4.08/1.99	
4.08/1.99	----------------------------------------
4.08/1.99	
4.08/1.99	(0)
4.08/1.99	Obligation:
4.08/1.99	Complexity Int TRS consisting of the following rules:
4.08/1.99	f0(A, B, C, D, E) -> Com_1(f7(400, 0, C, D, E)) :|: TRUE
4.08/1.99	f7(A, B, C, D, E) -> Com_1(f10(A, B, 0, D, E)) :|: 4 >= B
4.08/1.99	f10(A, B, C, D, E) -> Com_1(f13(A, B, C, 0, E)) :|: 4 >= C
4.08/1.99	f13(A, B, C, D, E) -> Com_1(f16(A, B, C, D, 0)) :|: 4 >= D
4.08/1.99	f16(A, B, C, D, E) -> Com_1(f16(A, B, C, D, E + 1)) :|: 4 >= E && A >= F + 1
4.08/1.99	f16(A, B, C, D, E) -> Com_1(f16(A, B, C, D, E + 1)) :|: 4 >= E
4.08/1.99	f16(A, B, C, D, E) -> Com_1(f31(A, B, C, D, E)) :|: 4 >= E
4.08/1.99	f16(A, B, C, D, E) -> Com_1(f13(A, B, C, D + 1, E)) :|: E >= 5
4.08/1.99	f13(A, B, C, D, E) -> Com_1(f10(A, B, C + 1, D, E)) :|: D >= 5
4.08/1.99	f10(A, B, C, D, E) -> Com_1(f7(A, B + 1, C, D, E)) :|: C >= 5
4.08/1.99	f7(A, B, C, D, E) -> Com_1(f31(A, B, C, D, E)) :|: B >= 5
4.08/1.99	
4.08/1.99	The start-symbols are:[f0_5]
4.08/1.99	
4.08/1.99	
4.08/1.99	----------------------------------------
4.08/1.99	
4.08/1.99	(1) Koat Proof (FINISHED)
4.08/1.99	YES(?, 1563)
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	Initial complexity problem:
4.08/1.99	
4.08/1.99	1:	T:
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.08/1.99	
4.08/1.99	2:	T:
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	A polynomial rank function with
4.08/1.99	
4.08/1.99		Pol(f0) = 1
4.08/1.99	
4.08/1.99		Pol(f7) = 1
4.08/1.99	
4.08/1.99		Pol(f10) = 1
4.08/1.99	
4.08/1.99		Pol(f13) = 1
4.08/1.99	
4.08/1.99		Pol(f16) = 1
4.08/1.99	
4.08/1.99		Pol(f31) = 0
4.08/1.99	
4.08/1.99		Pol(koat_start) = 1
4.08/1.99	
4.08/1.99	orients all transitions weakly and the transitions
4.08/1.99	
4.08/1.99		f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99	strictly and produces the following problem:
4.08/1.99	
4.08/1.99	3:	T:
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	A polynomial rank function with
4.08/1.99	
4.08/1.99		Pol(f0) = 5
4.08/1.99	
4.08/1.99		Pol(f7) = -V_2 + 5
4.08/1.99	
4.08/1.99		Pol(f10) = -V_2 + 4
4.08/1.99	
4.08/1.99		Pol(f13) = -V_2 + 4
4.08/1.99	
4.08/1.99		Pol(f16) = -V_2 + 4
4.08/1.99	
4.08/1.99		Pol(f31) = -V_2 + 4
4.08/1.99	
4.08/1.99		Pol(koat_start) = 5
4.08/1.99	
4.08/1.99	orients all transitions weakly and the transition
4.08/1.99	
4.08/1.99		f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99	strictly and produces the following problem:
4.08/1.99	
4.08/1.99	4:	T:
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: 5, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	A polynomial rank function with
4.08/1.99	
4.08/1.99		Pol(f16) = 1
4.08/1.99	
4.08/1.99		Pol(f13) = 1
4.08/1.99	
4.08/1.99		Pol(f10) = 1
4.08/1.99	
4.08/1.99		Pol(f7) = 0
4.08/1.99	
4.08/1.99	and size complexities
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/1.99	
4.08/1.99	orients the transitions
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99		f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99		f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99	weakly and the transition
4.08/1.99	
4.08/1.99		f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99	strictly and produces the following problem:
4.08/1.99	
4.08/1.99	5:	T:
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: 5, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 5, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)    f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	A polynomial rank function with
4.08/1.99	
4.08/1.99		Pol(f16) = -V_3 + 4
4.08/1.99	
4.08/1.99		Pol(f13) = -V_3 + 4
4.08/1.99	
4.08/1.99		Pol(f10) = -V_3 + 5
4.08/1.99	
4.08/1.99	and size complexities
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/1.99	
4.08/1.99		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/1.99	
4.08/1.99	orients the transitions
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99		f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99	weakly and the transition
4.08/1.99	
4.08/1.99		f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99	strictly and produces the following problem:
4.08/1.99	
4.08/1.99	6:	T:
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/1.99	
4.08/1.99			(Comp: 5, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/1.99	
4.08/1.99			(Comp: 25, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 5, Cost: 1)     f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/1.99	
4.08/1.99			(Comp: 1, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/1.99	
4.08/1.99			(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 ]
4.08/1.99	
4.08/1.99		start location:	koat_start
4.08/1.99	
4.08/1.99		leaf cost:	0
4.08/1.99	
4.08/1.99	
4.08/1.99	
4.08/1.99	A polynomial rank function with
4.08/1.99	
4.08/1.99		Pol(f16) = 1
4.08/1.99	
4.08/1.99		Pol(f13) = 1
4.08/1.99	
4.08/1.99		Pol(f10) = 0
4.08/1.99	
4.08/1.99	and size complexities
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		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
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/1.99	
4.08/1.99		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = ?
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/2.00	
4.08/2.00	orients the transitions
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00	weakly and the transition
4.08/2.00	
4.08/2.00		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00	strictly and produces the following problem:
4.08/2.00	
4.08/2.00	7:	T:
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)    f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)     f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)     f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)     f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/2.00	
4.08/2.00			(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 ]
4.08/2.00	
4.08/2.00		start location:	koat_start
4.08/2.00	
4.08/2.00		leaf cost:	0
4.08/2.00	
4.08/2.00	
4.08/2.00	
4.08/2.00	A polynomial rank function with
4.08/2.00	
4.08/2.00		Pol(f16) = -V_4 + 4
4.08/2.00	
4.08/2.00		Pol(f13) = -V_4 + 5
4.08/2.00	
4.08/2.00	and size complexities
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/2.00	
4.08/2.00	orients the transitions
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00	weakly and the transition
4.08/2.00	
4.08/2.00		f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00	strictly and produces the following problem:
4.08/2.00	
4.08/2.00	8:	T:
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/2.00	
4.08/2.00			(Comp: 125, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/2.00	
4.08/2.00			(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 ]
4.08/2.00	
4.08/2.00		start location:	koat_start
4.08/2.00	
4.08/2.00		leaf cost:	0
4.08/2.00	
4.08/2.00	
4.08/2.00	
4.08/2.00	A polynomial rank function with
4.08/2.00	
4.08/2.00		Pol(f16) = 1
4.08/2.00	
4.08/2.00		Pol(f13) = 0
4.08/2.00	
4.08/2.00	and size complexities
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ?
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/2.00	
4.08/2.00	orients the transitions
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00	weakly and the transition
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00	strictly and produces the following problem:
4.08/2.00	
4.08/2.00	9:	T:
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/2.00	
4.08/2.00			(Comp: 125, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00			(Comp: ?, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 125, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/2.00	
4.08/2.00			(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 ]
4.08/2.00	
4.08/2.00		start location:	koat_start
4.08/2.00	
4.08/2.00		leaf cost:	0
4.08/2.00	
4.08/2.00	
4.08/2.00	
4.08/2.00	A polynomial rank function with
4.08/2.00	
4.08/2.00		Pol(f16) = -V_5 + 5
4.08/2.00	
4.08/2.00	and size complexities
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		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
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\\ ar_0 >= f + 1 ]", 0-4) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-3) = 125
4.08/2.00	
4.08/2.00		S("f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]", 0-4) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-2) = 25
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-3) = 0
4.08/2.00	
4.08/2.00		S("f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]", 0-4) = ar_4 + 10
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-1) = 5
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-2) = 0
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-3) = ar_3 + 125
4.08/2.00	
4.08/2.00		S("f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]", 0-4) = ar_4 + 5
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-0) = 400
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-1) = 0
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.08/2.00	
4.08/2.00		S("f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.08/2.00	
4.08/2.00	orients the transitions
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00	weakly and the transitions
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00		f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00	strictly and produces the following problem:
4.08/2.00	
4.08/2.00	10:	T:
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(400, 0, ar_2, ar_3, ar_4))
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, 0, ar_3, ar_4)) [ 4 >= ar_1 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, 0, ar_4)) [ 4 >= ar_2 ]
4.08/2.00	
4.08/2.00			(Comp: 125, Cost: 1)    f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, 0)) [ 4 >= ar_3 ]
4.08/2.00	
4.08/2.00			(Comp: 625, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 /\ ar_0 >= f + 1 ]
4.08/2.00	
4.08/2.00			(Comp: 625, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f16(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 4 >= ar_4 ]
4.08/2.00	
4.08/2.00			(Comp: 125, Cost: 1)    f16(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f13(ar_0, ar_1, ar_2, ar_3 + 1, ar_4)) [ ar_4 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 25, Cost: 1)     f13(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f10(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_3 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 5, Cost: 1)      f10(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f7(ar_0, ar_1 + 1, ar_2, ar_3, ar_4)) [ ar_2 >= 5 ]
4.08/2.00	
4.08/2.00			(Comp: 1, Cost: 1)      f7(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(f31(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 5 ]
4.08/2.00	
4.08/2.00			(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 ]
4.08/2.00	
4.08/2.00		start location:	koat_start
4.08/2.00	
4.08/2.00		leaf cost:	0
4.08/2.00	
4.08/2.00	
4.08/2.00	
4.08/2.00	Complexity upper bound 1563
4.08/2.00	
4.08/2.00	
4.08/2.00	
4.08/2.00	Time: 0.277 sec (SMT: 0.213 sec)
4.08/2.00	
4.08/2.00	
4.08/2.00	----------------------------------------
4.08/2.00	
4.08/2.00	(2)
4.08/2.00	BOUNDS(1, 1)
4.34/2.02	EOF