3.58/1.87	WORST_CASE(?, O(1))
3.92/1.88	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
3.92/1.88	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.92/1.88	
3.92/1.88	
3.92/1.88	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
3.92/1.88	
3.92/1.88	(0) CpxIntTrs
3.92/1.88	(1) Koat Proof [FINISHED, 99 ms]
3.92/1.88	(2) BOUNDS(1, 1)
3.92/1.88	
3.92/1.88	
3.92/1.88	----------------------------------------
3.92/1.88	
3.92/1.88	(0)
3.92/1.88	Obligation:
3.92/1.88	Complexity Int TRS consisting of the following rules:
3.92/1.88	f0(A, B, C) -> Com_1(f8(0, B, C)) :|: TRUE
3.92/1.88	f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 0 >= A && 0 >= D
3.92/1.88	f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 0 >= A
3.92/1.88	f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 0 >= A && 0 >= E + 1
3.92/1.88	f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 0 >= A
3.92/1.88	f23(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 0 >= A
3.92/1.88	f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: TRUE
3.92/1.88	f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 0 >= D + 1
3.92/1.88	f23(A, B, C) -> Com_1(f38(A, B, C)) :|: A >= 1
3.92/1.88	f8(A, B, C) -> Com_1(f8(A + 1, A, C)) :|: 0 >= A
3.92/1.88	f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: TRUE
3.92/1.88	f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: 0 >= D + 1
3.92/1.88	f8(A, B, C) -> Com_1(f23(0, B, C)) :|: A >= 1
3.92/1.88	
3.92/1.88	The start-symbols are:[f0_3]
3.92/1.88	
3.92/1.88	
3.92/1.88	----------------------------------------
3.92/1.88	
3.92/1.88	(1) Koat Proof (FINISHED)
3.92/1.88	YES(?, 19)
3.92/1.88	
3.92/1.88	
3.92/1.88	
3.92/1.88	Initial complexity problem:
3.92/1.88	
3.92/1.88	1:	T:
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f8(0, ar_1, ar_2))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f38(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_0, ar_2)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f23(0, ar_1, ar_2)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
3.92/1.88	
3.92/1.88		start location:	koat_start
3.92/1.88	
3.92/1.88		leaf cost:	0
3.92/1.88	
3.92/1.88	
3.92/1.88	
3.92/1.88	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0].
3.92/1.88	
3.92/1.88	We thus obtain the following problem:
3.92/1.88	
3.92/1.88	2:	T:
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.88	
3.92/1.88		start location:	koat_start
3.92/1.88	
3.92/1.88		leaf cost:	0
3.92/1.88	
3.92/1.88	
3.92/1.88	
3.92/1.88	Repeatedly propagating knowledge in problem 2 produces the following problem:
3.92/1.88	
3.92/1.88	3:	T:
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.88	
3.92/1.88		start location:	koat_start
3.92/1.88	
3.92/1.88		leaf cost:	0
3.92/1.88	
3.92/1.88	
3.92/1.88	
3.92/1.88	A polynomial rank function with
3.92/1.88	
3.92/1.88		Pol(koat_start) = 2
3.92/1.88	
3.92/1.88		Pol(f0) = 2
3.92/1.88	
3.92/1.88		Pol(f8) = 2
3.92/1.88	
3.92/1.88		Pol(f23) = 1
3.92/1.88	
3.92/1.88		Pol(f14) = 2
3.92/1.88	
3.92/1.88		Pol(f38) = 0
3.92/1.88	
3.92/1.88		Pol(f28) = 1
3.92/1.88	
3.92/1.88	orients all transitions weakly and the transitions
3.92/1.88	
3.92/1.88		f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88		f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88	strictly and produces the following problem:
3.92/1.88	
3.92/1.88	4:	T:
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.88	
3.92/1.88			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.88	
3.92/1.88		start location:	koat_start
3.92/1.88	
3.92/1.88		leaf cost:	0
3.92/1.88	
3.92/1.88	
3.92/1.88	
3.92/1.88	A polynomial rank function with
3.92/1.88	
3.92/1.88		Pol(koat_start) = 1
3.92/1.88	
3.92/1.88		Pol(f0) = 1
3.92/1.88	
3.92/1.88		Pol(f8) = 1
3.92/1.88	
3.92/1.88		Pol(f23) = -V_1 + 1
3.92/1.88	
3.92/1.88		Pol(f14) = 1
3.92/1.88	
3.92/1.88		Pol(f38) = -V_1
3.92/1.88	
3.92/1.88		Pol(f28) = -V_1
3.92/1.88	
3.92/1.88	orients all transitions weakly and the transitions
3.92/1.88	
3.92/1.88		f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.88	
3.92/1.88		f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88		f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88	strictly and produces the following problem:
3.92/1.88	
3.92/1.88	5:	T:
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.88	
3.92/1.88			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.88	
3.92/1.88			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.88	
3.92/1.88			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.88	
3.92/1.88			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.89	
3.92/1.89		start location:	koat_start
3.92/1.89	
3.92/1.89		leaf cost:	0
3.92/1.89	
3.92/1.89	
3.92/1.89	
3.92/1.89	Repeatedly propagating knowledge in problem 5 produces the following problem:
3.92/1.89	
3.92/1.89	6:	T:
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.89	
3.92/1.89		start location:	koat_start
3.92/1.89	
3.92/1.89		leaf cost:	0
3.92/1.89	
3.92/1.89	
3.92/1.89	
3.92/1.89	A polynomial rank function with
3.92/1.89	
3.92/1.89		Pol(f8) = -V_1 + 1
3.92/1.89	
3.92/1.89		Pol(f14) = -V_1
3.92/1.89	
3.92/1.89	and size complexities
3.92/1.89	
3.92/1.89		S("f0(ar_0) -> Com_1(f8(0))", 0-0) = 0
3.92/1.89	
3.92/1.89		S("f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\\ 0 >= d ]", 0-0) = ?
3.92/1.89	
3.92/1.89		S("f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]", 0-0) = ?
3.92/1.89	
3.92/1.89		S("f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\\ 0 >= e + 1 ]", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f28(ar_0) -> Com_1(f23(ar_0 + 1))", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]", 0-0) = 5
3.92/1.89	
3.92/1.89		S("f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]", 0-0) = ?
3.92/1.89	
3.92/1.89		S("f14(ar_0) -> Com_1(f8(ar_0 + 1))", 0-0) = ?
3.92/1.89	
3.92/1.89		S("f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]", 0-0) = ?
3.92/1.89	
3.92/1.89		S("f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]", 0-0) = 0
3.92/1.89	
3.92/1.89		S("koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]", 0-0) = ar_0
3.92/1.89	
3.92/1.89	orients the transitions
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89		f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89		f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.89	
3.92/1.89	weakly and the transitions
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89		f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89	strictly and produces the following problem:
3.92/1.89	
3.92/1.89	7:	T:
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.89	
3.92/1.89		start location:	koat_start
3.92/1.89	
3.92/1.89		leaf cost:	0
3.92/1.89	
3.92/1.89	
3.92/1.89	
3.92/1.89	Repeatedly propagating knowledge in problem 7 produces the following problem:
3.92/1.89	
3.92/1.89	8:	T:
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= d + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 2, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 0 >= ar_0 /\ 0 >= e + 1 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 0 >= ar_0 /\ 0 >= d ]
3.92/1.89	
3.92/1.89			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
3.92/1.89	
3.92/1.89		start location:	koat_start
3.92/1.89	
3.92/1.89		leaf cost:	0
3.92/1.89	
3.92/1.89	
3.92/1.89	
3.92/1.89	Complexity upper bound 19
3.92/1.89	
3.92/1.89	
3.92/1.89	
3.92/1.89	Time: 0.162 sec (SMT: 0.153 sec)
3.92/1.89	
3.92/1.89	
3.92/1.89	----------------------------------------
3.92/1.89	
3.92/1.89	(2)
3.92/1.89	BOUNDS(1, 1)
3.94/1.91	EOF