3.47/1.88	WORST_CASE(?, O(1))
3.47/1.89	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.47/1.89	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.47/1.89	
3.47/1.89	
3.47/1.89	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.47/1.89	
3.47/1.89	(0) CpxIntTrs
3.47/1.89	(1) Koat Proof [FINISHED, 117 ms]
3.47/1.89	(2) BOUNDS(1, 1)
3.47/1.89	
3.47/1.89	
3.47/1.89	----------------------------------------
3.47/1.89	
3.47/1.89	(0)
3.47/1.89	Obligation:
3.47/1.89	Complexity Int TRS consisting of the following rules:
3.47/1.89	f0(A, B, C) -> Com_1(f10(1, B, C)) :|: TRUE
3.47/1.89	f10(A, B, C) -> Com_1(f13(A, 1, C)) :|: 5 >= A
3.47/1.89	f13(A, B, C) -> Com_1(f13(A, B + 1, C)) :|: 5 >= B
3.47/1.89	f21(A, B, C) -> Com_1(f24(A, 1, C)) :|: 5 >= A
3.47/1.89	f24(A, B, C) -> Com_1(f27(A, B, 1)) :|: 5 >= B
3.47/1.89	f27(A, B, C) -> Com_1(f27(A, B, C + 1)) :|: 5 >= C
3.47/1.89	f27(A, B, C) -> Com_1(f24(A, B + 1, C)) :|: C >= 6
3.47/1.89	f24(A, B, C) -> Com_1(f21(A + 1, B, C)) :|: B >= 6
3.47/1.89	f21(A, B, C) -> Com_1(f39(A, B, C)) :|: A >= 6
3.47/1.89	f13(A, B, C) -> Com_1(f10(A + 1, B, C)) :|: B >= 6
3.47/1.89	f10(A, B, C) -> Com_1(f21(1, B, C)) :|: A >= 6
3.47/1.89	
3.47/1.89	The start-symbols are:[f0_3]
3.47/1.89	
3.47/1.89	
3.47/1.89	----------------------------------------
3.47/1.89	
3.47/1.89	(1) Koat Proof (FINISHED)
3.47/1.89	YES(?, 1443)
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	Initial complexity problem:
3.47/1.89	
3.47/1.89	1:	T:
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.89	
3.47/1.89		start location:	koat_start
3.47/1.89	
3.47/1.89		leaf cost:	0
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	Repeatedly propagating knowledge in problem 1 produces the following problem:
3.47/1.89	
3.47/1.89	2:	T:
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.89	
3.47/1.89		start location:	koat_start
3.47/1.89	
3.47/1.89		leaf cost:	0
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	A polynomial rank function with
3.47/1.89	
3.47/1.89		Pol(f0) = 2
3.47/1.89	
3.47/1.89		Pol(f10) = 2
3.47/1.89	
3.47/1.89		Pol(f13) = 2
3.47/1.89	
3.47/1.89		Pol(f21) = 1
3.47/1.89	
3.47/1.89		Pol(f24) = 1
3.47/1.89	
3.47/1.89		Pol(f27) = 1
3.47/1.89	
3.47/1.89		Pol(f39) = 0
3.47/1.89	
3.47/1.89		Pol(koat_start) = 2
3.47/1.89	
3.47/1.89	orients all transitions weakly and the transitions
3.47/1.89	
3.47/1.89		f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89		f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89	strictly and produces the following problem:
3.47/1.89	
3.47/1.89	3:	T:
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.89	
3.47/1.89		start location:	koat_start
3.47/1.89	
3.47/1.89		leaf cost:	0
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	A polynomial rank function with
3.47/1.89	
3.47/1.89		Pol(f0) = 5
3.47/1.89	
3.47/1.89		Pol(f10) = 5
3.47/1.89	
3.47/1.89		Pol(f13) = 5
3.47/1.89	
3.47/1.89		Pol(f21) = -V_1 + 6
3.47/1.89	
3.47/1.89		Pol(f24) = -V_1 + 5
3.47/1.89	
3.47/1.89		Pol(f27) = -V_1 + 5
3.47/1.89	
3.47/1.89		Pol(f39) = -V_1 + 6
3.47/1.89	
3.47/1.89		Pol(koat_start) = 5
3.47/1.89	
3.47/1.89	orients all transitions weakly and the transition
3.47/1.89	
3.47/1.89		f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89	strictly and produces the following problem:
3.47/1.89	
3.47/1.89	4:	T:
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: 5, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.89	
3.47/1.89		start location:	koat_start
3.47/1.89	
3.47/1.89		leaf cost:	0
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	A polynomial rank function with
3.47/1.89	
3.47/1.89		Pol(f27) = 1
3.47/1.89	
3.47/1.89		Pol(f24) = 1
3.47/1.89	
3.47/1.89		Pol(f21) = 0
3.47/1.89	
3.47/1.89		Pol(f13) = 0
3.47/1.89	
3.47/1.89		Pol(f10) = 0
3.47/1.89	
3.47/1.89	and size complexities
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 1
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-2) = 1
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2 + 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-0) = 1
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-1) = ar_1
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-2) = ar_2
3.47/1.89	
3.47/1.89	orients the transitions
3.47/1.89	
3.47/1.89		f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89		f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89		f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89		f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89		f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89		f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89		f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89	weakly and the transition
3.47/1.89	
3.47/1.89		f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89	strictly and produces the following problem:
3.47/1.89	
3.47/1.89	5:	T:
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: 5, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 5, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: ?, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 2, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.89	
3.47/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.89	
3.47/1.89		start location:	koat_start
3.47/1.89	
3.47/1.89		leaf cost:	0
3.47/1.89	
3.47/1.89	
3.47/1.89	
3.47/1.89	A polynomial rank function with
3.47/1.89	
3.47/1.89		Pol(f27) = -V_2 + 5
3.47/1.89	
3.47/1.89		Pol(f24) = -V_2 + 6
3.47/1.89	
3.47/1.89		Pol(f13) = -V_1 + 5
3.47/1.89	
3.47/1.89		Pol(f10) = -V_1 + 6
3.47/1.89	
3.47/1.89	and size complexities
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
3.47/1.89	
3.47/1.89		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 1
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-2) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-1) = ?
3.47/1.89	
3.47/1.89		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-2) = 1
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = 6
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.89	
3.47/1.89		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2 + 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-1) = 6
3.47/1.89	
3.47/1.89		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = ?
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.89	
3.47/1.89		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-0) = 1
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-1) = ar_1
3.47/1.89	
3.47/1.89		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-2) = ar_2
3.47/1.89	
3.47/1.89	orients the transitions
3.47/1.89	
3.47/1.89		f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.89	
3.47/1.89		f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.89	
3.47/1.89		f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89		f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89		f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.89	
3.47/1.89		f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.89	
3.47/1.89	weakly and the transitions
3.47/1.89	
3.47/1.89		f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.89	
3.47/1.89		f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90	strictly and produces the following problem:
3.47/1.90	
3.47/1.90	6:	T:
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)     f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)     f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)     f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)     f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.90	
3.47/1.90		start location:	koat_start
3.47/1.90	
3.47/1.90		leaf cost:	0
3.47/1.90	
3.47/1.90	
3.47/1.90	
3.47/1.90	A polynomial rank function with
3.47/1.90	
3.47/1.90		Pol(f27) = 1
3.47/1.90	
3.47/1.90		Pol(f24) = 0
3.47/1.90	
3.47/1.90		Pol(f13) = 1
3.47/1.90	
3.47/1.90		Pol(f10) = 0
3.47/1.90	
3.47/1.90	and size complexities
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 1
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = ?
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = ?
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = ?
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-1) = ?
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-1) = ?
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-1) = ?
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-2) = 1
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2 + 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-0) = ?
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = ?
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-0) = 1
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-1) = ar_1
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-2) = ar_2
3.47/1.90	
3.47/1.90	orients the transitions
3.47/1.90	
3.47/1.90		f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90		f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.90	
3.47/1.90		f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90		f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90	weakly and the transitions
3.47/1.90	
3.47/1.90		f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.90	
3.47/1.90		f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90	strictly and produces the following problem:
3.47/1.90	
3.47/1.90	7:	T:
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 1)     f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)    f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)     f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)    f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: ?, Cost: 1)     f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90			(Comp: 84, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)     f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)     f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 84, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)     f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 0)     koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.90	
3.47/1.90		start location:	koat_start
3.47/1.90	
3.47/1.90		leaf cost:	0
3.47/1.90	
3.47/1.90	
3.47/1.90	
3.47/1.90	A polynomial rank function with
3.47/1.90	
3.47/1.90		Pol(f27) = -V_3 + 6
3.47/1.90	
3.47/1.90		Pol(f13) = -V_2 + 6
3.47/1.90	
3.47/1.90	and size complexities
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
3.47/1.90	
3.47/1.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 1
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = 85
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-1) = 85
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-1) = 85
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-1) = 85
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-1) = 85
3.47/1.90	
3.47/1.90		S("f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]", 0-2) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-1) = 85
3.47/1.90	
3.47/1.90		S("f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]", 0-2) = 1
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = 6
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.90	
3.47/1.90		S("f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2 + 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-0) = 85
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-1) = 6
3.47/1.90	
3.47/1.90		S("f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-0) = 85
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-1) = 1
3.47/1.90	
3.47/1.90		S("f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]", 0-2) = ar_2
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-0) = 1
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-1) = ar_1
3.47/1.90	
3.47/1.90		S("f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))", 0-2) = ar_2
3.47/1.90	
3.47/1.90	orients the transitions
3.47/1.90	
3.47/1.90		f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90		f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90	weakly and the transitions
3.47/1.90	
3.47/1.90		f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90		f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90	strictly and produces the following problem:
3.47/1.90	
3.47/1.90	8:	T:
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 1)      f0(ar_0, ar_1, ar_2) -> Com_1(f10(1, ar_1, ar_2))
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)     f10(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: 588, Cost: 1)    f13(ar_0, ar_1, ar_2) -> Com_1(f13(ar_0, ar_1 + 1, ar_2)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)      f21(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, 1, ar_2)) [ 5 >= ar_0 ]
3.47/1.90	
3.47/1.90			(Comp: 42, Cost: 1)     f24(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, 1)) [ 5 >= ar_1 ]
3.47/1.90	
3.47/1.90			(Comp: 588, Cost: 1)    f27(ar_0, ar_1, ar_2) -> Com_1(f27(ar_0, ar_1, ar_2 + 1)) [ 5 >= ar_2 ]
3.47/1.90	
3.47/1.90			(Comp: 84, Cost: 1)     f27(ar_0, ar_1, ar_2) -> Com_1(f24(ar_0, ar_1 + 1, ar_2)) [ ar_2 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 5, Cost: 1)      f24(ar_0, ar_1, ar_2) -> Com_1(f21(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)      f21(ar_0, ar_1, ar_2) -> Com_1(f39(ar_0, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 84, Cost: 1)     f13(ar_0, ar_1, ar_2) -> Com_1(f10(ar_0 + 1, ar_1, ar_2)) [ ar_1 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 2, Cost: 1)      f10(ar_0, ar_1, ar_2) -> Com_1(f21(1, ar_1, ar_2)) [ ar_0 >= 6 ]
3.47/1.90	
3.47/1.90			(Comp: 1, Cost: 0)      koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.47/1.90	
3.47/1.90		start location:	koat_start
3.47/1.90	
3.47/1.90		leaf cost:	0
3.47/1.90	
3.47/1.90	
3.47/1.90	
3.47/1.90	Complexity upper bound 1443
3.47/1.90	
3.47/1.90	
3.47/1.90	
3.47/1.90	Time: 0.181 sec (SMT: 0.159 sec)
3.47/1.90	
3.47/1.90	
3.47/1.90	----------------------------------------
3.47/1.90	
3.47/1.90	(2)
3.47/1.90	BOUNDS(1, 1)
4.14/1.91	EOF