3.47/1.83	WORST_CASE(?, O(1))
4.01/1.84	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.01/1.84	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.01/1.84	
4.01/1.84	
4.01/1.84	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, 1).
4.01/1.84	
4.01/1.84	(0) CpxIntTrs
4.01/1.84	(1) Koat Proof [FINISHED, 112 ms]
4.01/1.84	(2) BOUNDS(1, 1)
4.01/1.84	
4.01/1.84	
4.01/1.84	----------------------------------------
4.01/1.84	
4.01/1.84	(0)
4.01/1.84	Obligation:
4.01/1.84	Complexity Int TRS consisting of the following rules:
4.01/1.84	f0(A, B, C) -> Com_1(f8(0, B, C)) :|: TRUE
4.01/1.84	f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 9 >= A && 9 >= D
4.01/1.84	f8(A, B, C) -> Com_1(f14(A, A, C)) :|: 9 >= A
4.01/1.84	f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 9 >= A && 0 >= E + 1
4.01/1.84	f23(A, B, C) -> Com_1(f28(A, B, D)) :|: 9 >= A
4.01/1.84	f23(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 9 >= A
4.01/1.84	f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: TRUE
4.01/1.84	f28(A, B, C) -> Com_1(f23(A + 1, B, C)) :|: 8 >= D
4.01/1.84	f23(A, B, C) -> Com_1(f38(A, B, C)) :|: A >= 10
4.01/1.84	f8(A, B, C) -> Com_1(f8(A + 1, A, C)) :|: 9 >= A
4.01/1.84	f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: TRUE
4.01/1.84	f14(A, B, C) -> Com_1(f8(A + 1, B, C)) :|: 8 >= D
4.01/1.84	f8(A, B, C) -> Com_1(f23(0, B, C)) :|: A >= 10
4.01/1.84	
4.01/1.84	The start-symbols are:[f0_3]
4.01/1.84	
4.01/1.84	
4.01/1.84	----------------------------------------
4.01/1.84	
4.01/1.84	(1) Koat Proof (FINISHED)
4.01/1.84	YES(?, 145)
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Initial complexity problem:
4.01/1.84	
4.01/1.84	1:	T:
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f0(ar_0, ar_1, ar_2) -> Com_1(f8(0, ar_1, ar_2))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f14(ar_0, ar_0, ar_2)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f28(ar_0, ar_1, d)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0, ar_1, ar_2) -> Com_1(f23(ar_0 + 1, ar_1, ar_2)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0, ar_1, ar_2) -> Com_1(f38(ar_0, ar_1, ar_2)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_0, ar_2)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0, ar_1, ar_2) -> Com_1(f8(ar_0 + 1, ar_1, ar_2)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0, ar_1, ar_2) -> Com_1(f23(0, ar_1, ar_2)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(f0(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Slicing away variables that do not contribute to conditions from problem 1 leaves variables [ar_0].
4.01/1.84	
4.01/1.84	We thus obtain the following problem:
4.01/1.84	
4.01/1.84	2:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Repeatedly propagating knowledge in problem 2 produces the following problem:
4.01/1.84	
4.01/1.84	3:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	A polynomial rank function with
4.01/1.84	
4.01/1.84		Pol(koat_start) = 2
4.01/1.84	
4.01/1.84		Pol(f0) = 2
4.01/1.84	
4.01/1.84		Pol(f8) = 2
4.01/1.84	
4.01/1.84		Pol(f23) = 1
4.01/1.84	
4.01/1.84		Pol(f14) = 2
4.01/1.84	
4.01/1.84		Pol(f38) = 0
4.01/1.84	
4.01/1.84		Pol(f28) = 1
4.01/1.84	
4.01/1.84	orients all transitions weakly and the transitions
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84		f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84	strictly and produces the following problem:
4.01/1.84	
4.01/1.84	4:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)    koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)    f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)    f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)    f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	A polynomial rank function with
4.01/1.84	
4.01/1.84		Pol(koat_start) = 10
4.01/1.84	
4.01/1.84		Pol(f0) = 10
4.01/1.84	
4.01/1.84		Pol(f8) = 10
4.01/1.84	
4.01/1.84		Pol(f23) = -V_1 + 10
4.01/1.84	
4.01/1.84		Pol(f14) = 10
4.01/1.84	
4.01/1.84		Pol(f38) = -V_1
4.01/1.84	
4.01/1.84		Pol(f28) = -V_1 + 9
4.01/1.84	
4.01/1.84	orients all transitions weakly and the transitions
4.01/1.84	
4.01/1.84		f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84		f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84		f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84	strictly and produces the following problem:
4.01/1.84	
4.01/1.84	5:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)     koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)     f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Repeatedly propagating knowledge in problem 5 produces the following problem:
4.01/1.84	
4.01/1.84	6:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)     koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)     f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	A polynomial rank function with
4.01/1.84	
4.01/1.84		Pol(f8) = -V_1 + 10
4.01/1.84	
4.01/1.84		Pol(f14) = -V_1 + 9
4.01/1.84	
4.01/1.84	and size complexities
4.01/1.84	
4.01/1.84		S("f0(ar_0) -> Com_1(f8(0))", 0-0) = 0
4.01/1.84	
4.01/1.84		S("f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\\ 9 >= d ]", 0-0) = ?
4.01/1.84	
4.01/1.84		S("f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]", 0-0) = ?
4.01/1.84	
4.01/1.84		S("f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\\ 0 >= e + 1 ]", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f28(ar_0) -> Com_1(f23(ar_0 + 1))", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]", 0-0) = 50
4.01/1.84	
4.01/1.84		S("f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]", 0-0) = ?
4.01/1.84	
4.01/1.84		S("f14(ar_0) -> Com_1(f8(ar_0 + 1))", 0-0) = ?
4.01/1.84	
4.01/1.84		S("f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]", 0-0) = ?
4.01/1.84	
4.01/1.84		S("f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]", 0-0) = 0
4.01/1.84	
4.01/1.84		S("koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]", 0-0) = ar_0
4.01/1.84	
4.01/1.84	orients the transitions
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84		f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84		f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84	weakly and the transitions
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84		f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84	strictly and produces the following problem:
4.01/1.84	
4.01/1.84	7:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)     koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: ?, Cost: 1)     f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)     f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Repeatedly propagating knowledge in problem 7 produces the following problem:
4.01/1.84	
4.01/1.84	8:	T:
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 0)     koat_start(ar_0) -> Com_1(f0(ar_0)) [ 0 <= 0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f8(ar_0) -> Com_1(f23(0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f14(ar_0) -> Com_1(f8(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f8(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 2, Cost: 1)     f23(ar_0) -> Com_1(f38(ar_0)) [ ar_0 >= 10 ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1)) [ 8 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 20, Cost: 1)    f28(ar_0) -> Com_1(f23(ar_0 + 1))
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f23(ar_0 + 1)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f23(ar_0) -> Com_1(f28(ar_0)) [ 9 >= ar_0 /\ 0 >= e + 1 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 ]
4.01/1.84	
4.01/1.84			(Comp: 10, Cost: 1)    f8(ar_0) -> Com_1(f14(ar_0)) [ 9 >= ar_0 /\ 9 >= d ]
4.01/1.84	
4.01/1.84			(Comp: 1, Cost: 1)     f0(ar_0) -> Com_1(f8(0))
4.01/1.84	
4.01/1.84		start location:	koat_start
4.01/1.84	
4.01/1.84		leaf cost:	0
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Complexity upper bound 145
4.01/1.84	
4.01/1.84	
4.01/1.84	
4.01/1.84	Time: 0.157 sec (SMT: 0.147 sec)
4.01/1.84	
4.01/1.84	
4.01/1.84	----------------------------------------
4.01/1.84	
4.01/1.84	(2)
4.01/1.84	BOUNDS(1, 1)
4.01/1.86	EOF