4.82/2.32	WORST_CASE(Omega(n^1), O(n^1))
4.89/2.33	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
4.89/2.33	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.89/2.33	
4.89/2.33	
4.89/2.33	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.89/2.33	
4.89/2.33	(0) CpxIntTrs
4.89/2.33	(1) Koat Proof [FINISHED, 205 ms]
4.89/2.33	(2) BOUNDS(1, n^1)
4.89/2.33	(3) Loat Proof [FINISHED, 630 ms]
4.89/2.33	(4) BOUNDS(n^1, INF)
4.89/2.33	
4.89/2.33	
4.89/2.33	----------------------------------------
4.89/2.33	
4.89/2.33	(0)
4.89/2.33	Obligation:
4.89/2.33	Complexity Int TRS consisting of the following rules:
4.89/2.33	evalwisestart(A, B) -> Com_1(evalwiseentryin(A, B)) :|: TRUE
4.89/2.33	evalwiseentryin(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 0 >= A + 1
4.89/2.33	evalwiseentryin(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 0 >= B + 1
4.89/2.33	evalwiseentryin(A, B) -> Com_1(evalwisebb6in(B, A)) :|: A >= 0 && B >= 0
4.89/2.33	evalwisebb6in(A, B) -> Com_1(evalwisebb3in(A, B)) :|: B >= A + 3
4.89/2.33	evalwisebb6in(A, B) -> Com_1(evalwisebb3in(A, B)) :|: A >= B + 3
4.89/2.33	evalwisebb6in(A, B) -> Com_1(evalwisereturnin(A, B)) :|: 2 + A >= B && 2 + B >= A
4.89/2.33	evalwisebb3in(A, B) -> Com_1(evalwisebb4in(A, B)) :|: A >= B + 1
4.89/2.33	evalwisebb3in(A, B) -> Com_1(evalwisebb5in(A, B)) :|: B >= A
4.89/2.33	evalwisebb4in(A, B) -> Com_1(evalwisebb6in(A, B + 1)) :|: TRUE
4.89/2.33	evalwisebb5in(A, B) -> Com_1(evalwisebb6in(A + 1, B)) :|: TRUE
4.89/2.33	evalwisereturnin(A, B) -> Com_1(evalwisestop(A, B)) :|: TRUE
4.89/2.33	
4.89/2.33	The start-symbols are:[evalwisestart_2]
4.89/2.33	
4.89/2.33	
4.89/2.33	----------------------------------------
4.89/2.33	
4.89/2.33	(1) Koat Proof (FINISHED)
4.89/2.33	YES(?, 18*ar_1 + 18*ar_0 + 20)
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Initial complexity problem:
4.89/2.33	
4.89/2.33	1:	T:
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.89/2.33	
4.89/2.33	2:	T:
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	A polynomial rank function with
4.89/2.33	
4.89/2.33		Pol(evalwisestart) = 2
4.89/2.33	
4.89/2.33		Pol(evalwiseentryin) = 2
4.89/2.33	
4.89/2.33		Pol(evalwisereturnin) = 1
4.89/2.33	
4.89/2.33		Pol(evalwisebb6in) = 2
4.89/2.33	
4.89/2.33		Pol(evalwisebb3in) = 2
4.89/2.33	
4.89/2.33		Pol(evalwisebb4in) = 2
4.89/2.33	
4.89/2.33		Pol(evalwisebb5in) = 2
4.89/2.33	
4.89/2.33		Pol(evalwisestop) = 0
4.89/2.33	
4.89/2.33		Pol(koat_start) = 2
4.89/2.33	
4.89/2.33	orients all transitions weakly and the transitions
4.89/2.33	
4.89/2.33		evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33		evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33	strictly and produces the following problem:
4.89/2.33	
4.89/2.33	3:	T:
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)    evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Applied AI with 'oct' on problem 3 to obtain the following invariants:
4.89/2.33	
4.89/2.33	  For symbol evalwisebb3in: X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 >= 0
4.89/2.33	
4.89/2.33	  For symbol evalwisebb4in: X_1 - X_2 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 2 >= 0
4.89/2.33	
4.89/2.33	  For symbol evalwisebb5in: X_2 - 1 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0
4.89/2.33	
4.89/2.33	  For symbol evalwisebb6in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	This yielded the following problem:
4.89/2.33	
4.89/2.33	4:	T:
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)    evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)    evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	A polynomial rank function with
4.89/2.33	
4.89/2.33		Pol(evalwisebb5in) = -3*V_1 + 3*V_2 + 1
4.89/2.33	
4.89/2.33		Pol(evalwisebb6in) = -3*V_1 + 3*V_2 + 3
4.89/2.33	
4.89/2.33		Pol(evalwisebb3in) = -3*V_1 + 3*V_2 + 2
4.89/2.33	
4.89/2.33	and size complexities
4.89/2.33	
4.89/2.33		S("evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 3 ]", 0-0) = ?
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 3 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 3 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 3 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 + 2 >= ar_1 /\\ ar_1 + 2 >= ar_0 ]", 0-0) = ?
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 + 2 >= ar_1 /\\ ar_1 + 2 >= ar_0 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 ]", 0-0) = ?
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ?
4.89/2.33	
4.89/2.33		S("evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))", 0-0) = ?
4.89/2.33	
4.89/2.33		S("evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33	orients the transitions
4.89/2.33	
4.89/2.33		evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.89/2.33	
4.89/2.33		evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33		evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33	weakly and the transitions
4.89/2.33	
4.89/2.33		evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33		evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.89/2.33	
4.89/2.33		evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33	strictly and produces the following problem:
4.89/2.33	
4.89/2.33	5:	T:
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)                      evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)                      evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)                      evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)                      evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: ?, Cost: 1)                      evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	A polynomial rank function with
4.89/2.33	
4.89/2.33		Pol(evalwisebb6in) = 3*V_1 - 3*V_2 + 1
4.89/2.33	
4.89/2.33		Pol(evalwisebb3in) = 3*V_1 - 3*V_2
4.89/2.33	
4.89/2.33		Pol(evalwisebb4in) = 3*V_1 - 3*V_2 - 1
4.89/2.33	
4.89/2.33	and size complexities
4.89/2.33	
4.89/2.33		S("evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\\ ar_1 >= 0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 3 ]", 0-0) = 4*ar_0 + 4*ar_1 + 48
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 + 3 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 3 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 3 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 + 2 >= ar_1 /\\ ar_1 + 2 >= ar_0 ]", 0-0) = 4*ar_0 + 4*ar_1 + 192
4.89/2.33	
4.89/2.33		S("evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 /\\ ar_0 + 2 >= ar_1 /\\ ar_1 + 2 >= ar_0 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 + 1 ]", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 ]", 0-0) = 4*ar_0 + 4*ar_1 + 48
4.89/2.33	
4.89/2.33		S("evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 >= 0 /\\ ar_1 >= ar_0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-0) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\\ ar_1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 2 >= 0 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33		S("evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = 4*ar_0 + 4*ar_1 + 48
4.89/2.33	
4.89/2.33		S("evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
4.89/2.33	
4.89/2.33		S("evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))", 0-0) = 4*ar_0 + 4*ar_1 + 768
4.89/2.33	
4.89/2.33		S("evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))", 0-1) = ar_0 + ar_1
4.89/2.33	
4.89/2.33		S("koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]", 0-0) = ar_0
4.89/2.33	
4.89/2.33		S("koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]", 0-1) = ar_1
4.89/2.33	
4.89/2.33	orients the transitions
4.89/2.33	
4.89/2.33		evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33		evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ]
4.89/2.33	
4.89/2.33		evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33	weakly and the transitions
4.89/2.33	
4.89/2.33		evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33		evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ]
4.89/2.33	
4.89/2.33		evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33	strictly and produces the following problem:
4.89/2.33	
4.89/2.33	6:	T:
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1) -> Com_1(evalwisestart(ar_0, ar_1)) [ 0 <= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)                      evalwisereturnin(ar_0, ar_1) -> Com_1(evalwisestop(ar_0, ar_1))
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb5in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 1, Cost: 1)    evalwisebb4in(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_0, ar_1 + 1)) [ ar_0 - ar_1 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 2 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb5in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 1, Cost: 1)    evalwisebb3in(ar_0, ar_1) -> Com_1(evalwisebb4in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 2, Cost: 1)                      evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 + 2 >= ar_1 /\ ar_1 + 2 >= ar_0 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 1, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 3*ar_1 + 3*ar_0 + 3, Cost: 1)    evalwisebb6in(ar_0, ar_1) -> Com_1(evalwisebb3in(ar_0, ar_1)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_0 + 3 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisebb6in(ar_1, ar_0)) [ ar_0 >= 0 /\ ar_1 >= 0 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_1 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwiseentryin(ar_0, ar_1) -> Com_1(evalwisereturnin(ar_0, ar_1)) [ 0 >= ar_0 + 1 ]
4.89/2.33	
4.89/2.33			(Comp: 1, Cost: 1)                      evalwisestart(ar_0, ar_1) -> Com_1(evalwiseentryin(ar_0, ar_1))
4.89/2.33	
4.89/2.33		start location:	koat_start
4.89/2.33	
4.89/2.33		leaf cost:	0
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Complexity upper bound 18*ar_1 + 18*ar_0 + 20
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Time: 0.246 sec (SMT: 0.210 sec)
4.89/2.33	
4.89/2.33	
4.89/2.33	----------------------------------------
4.89/2.33	
4.89/2.33	(2)
4.89/2.33	BOUNDS(1, n^1)
4.89/2.33	
4.89/2.33	----------------------------------------
4.89/2.33	
4.89/2.33	(3) Loat Proof (FINISHED)
4.89/2.33	
4.89/2.33	
4.89/2.33	### Pre-processing the ITS problem ###
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Initial linear ITS problem
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	      0: evalwisestart -> evalwiseentryin : [], cost: 1
4.89/2.33	
4.89/2.33	      1: evalwiseentryin -> evalwisereturnin : [ 0>=1+A ], cost: 1
4.89/2.33	
4.89/2.33	      2: evalwiseentryin -> evalwisereturnin : [ 0>=1+B ], cost: 1
4.89/2.33	
4.89/2.33	      3: evalwiseentryin -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 1
4.89/2.33	
4.89/2.33	      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1
4.89/2.33	
4.89/2.33	      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1
4.89/2.33	
4.89/2.33	      6: evalwisebb6in -> evalwisereturnin : [ 2+A>=B && 2+B>=A ], cost: 1
4.89/2.33	
4.89/2.33	      7: evalwisebb3in -> evalwisebb4in : [ A>=1+B ], cost: 1
4.89/2.33	
4.89/2.33	      8: evalwisebb3in -> evalwisebb5in : [ B>=A ], cost: 1
4.89/2.33	
4.89/2.33	      9: evalwisebb4in -> evalwisebb6in : B'=1+B, [], cost: 1
4.89/2.33	
4.89/2.33	     10: evalwisebb5in -> evalwisebb6in : A'=1+A, [], cost: 1
4.89/2.33	
4.89/2.33	     11: evalwisereturnin -> evalwisestop : [], cost: 1
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Removed unreachable and leaf rules:
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	      0: evalwisestart -> evalwiseentryin : [], cost: 1
4.89/2.33	
4.89/2.33	      3: evalwiseentryin -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 1
4.89/2.33	
4.89/2.33	      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1
4.89/2.33	
4.89/2.33	      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1
4.89/2.33	
4.89/2.33	      7: evalwisebb3in -> evalwisebb4in : [ A>=1+B ], cost: 1
4.89/2.33	
4.89/2.33	      8: evalwisebb3in -> evalwisebb5in : [ B>=A ], cost: 1
4.89/2.33	
4.89/2.33	      9: evalwisebb4in -> evalwisebb6in : B'=1+B, [], cost: 1
4.89/2.33	
4.89/2.33	     10: evalwisebb5in -> evalwisebb6in : A'=1+A, [], cost: 1
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	### Simplification by acceleration and chaining ###
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Eliminated locations (on linear paths):
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2
4.89/2.33	
4.89/2.33	      4: evalwisebb6in -> evalwisebb3in : [ B>=3+A ], cost: 1
4.89/2.33	
4.89/2.33	      5: evalwisebb6in -> evalwisebb3in : [ A>=3+B ], cost: 1
4.89/2.33	
4.89/2.33	     13: evalwisebb3in -> evalwisebb6in : B'=1+B, [ A>=1+B ], cost: 2
4.89/2.33	
4.89/2.33	     14: evalwisebb3in -> evalwisebb6in : A'=1+A, [ B>=A ], cost: 2
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Eliminated locations (on tree-shaped paths):
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2
4.89/2.33	
4.89/2.33	     15: evalwisebb6in -> evalwisebb6in : A'=1+A, [ B>=3+A ], cost: 3
4.89/2.33	
4.89/2.33	     16: evalwisebb6in -> evalwisebb6in : B'=1+B, [ A>=3+B ], cost: 3
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Accelerating simple loops of location 2.
4.89/2.33	
4.89/2.33	   Accelerating the following rules:
4.89/2.33	
4.89/2.33	     15: evalwisebb6in -> evalwisebb6in : A'=1+A, [ B>=3+A ], cost: 3
4.89/2.33	
4.89/2.33	     16: evalwisebb6in -> evalwisebb6in : B'=1+B, [ A>=3+B ], cost: 3
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	   Accelerated rule 15 with metering function -2-A+B, yielding the new rule 17.
4.89/2.33	
4.89/2.33	   Accelerated rule 16 with metering function -2+A-B, yielding the new rule 18.
4.89/2.33	
4.89/2.33	   Removing the simple loops: 15 16.
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Accelerated all simple loops using metering functions (where possible):
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2
4.89/2.33	
4.89/2.33	     17: evalwisebb6in -> evalwisebb6in : A'=-2+B, [ B>=3+A ], cost: -6-3*A+3*B
4.89/2.33	
4.89/2.33	     18: evalwisebb6in -> evalwisebb6in : B'=-2+A, [ A>=3+B ], cost: -6+3*A-3*B
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Chained accelerated rules (with incoming rules):
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     12: evalwisestart -> evalwisebb6in : A'=B, B'=A, [ A>=0 && B>=0 ], cost: 2
4.89/2.33	
4.89/2.33	     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B
4.89/2.33	
4.89/2.33	     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Removed unreachable locations (and leaf rules with constant cost):
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B
4.89/2.33	
4.89/2.33	     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	### Computing asymptotic complexity ###
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Fully simplified ITS problem
4.89/2.33	
4.89/2.33	   Start location: evalwisestart
4.89/2.33	
4.89/2.33	     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ A>=0 && B>=0 && A>=3+B ], cost: -4+3*A-3*B
4.89/2.33	
4.89/2.33	     20: evalwisestart -> evalwisebb6in : A'=B, B'=-2+B, [ A>=0 && B>=0 && B>=3+A ], cost: -4-3*A+3*B
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Computing asymptotic complexity for rule 19
4.89/2.33	
4.89/2.33	   Simplified the guard:
4.89/2.33	
4.89/2.33	     19: evalwisestart -> evalwisebb6in : A'=-2+A, B'=A, [ B>=0 && A>=3+B ], cost: -4+3*A-3*B
4.89/2.33	
4.89/2.33	   Solved the limit problem by the following transformations:
4.89/2.33	
4.89/2.33	      Created initial limit problem:
4.89/2.33	
4.89/2.33	      1+B (+/+!), -2+A-B (+/+!), -4+3*A-3*B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (C) using substitution {B==0}
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      1 (+/+!), -4+3*A (+), -2+A (+/+!) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (C) using substitution {A==3+B}
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      1 (+/+!), 1+B (+/+!), 5+3*B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (B), deleting 1 (+/+!)
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      1+B (+/+!), 5+3*B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (D), replacing 1+B (+/+!) by B (+)
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      5+3*B (+), B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (D), replacing 5+3*B (+) by 3*B (+)
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      3*B (+), B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (A), replacing 3*B (+) by B (+) and 3 (+!) using + limit vector (+,+!)
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      3 (+!), B (+) [not solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	      applying transformation rule (B), deleting 3 (+!)
4.89/2.33	
4.89/2.33	      resulting limit problem:
4.89/2.33	
4.89/2.33	      B (+) [solved]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	   Solution:
4.89/2.33	
4.89/2.33	      A / 3+n
4.89/2.33	
4.89/2.33	      B / 0
4.89/2.33	
4.89/2.33	   Resulting cost 5+3*n has complexity: Poly(n^1)
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Found new complexity Poly(n^1).
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	Obtained the following overall complexity (w.r.t. the length of the input n):
4.89/2.33	
4.89/2.33	   Complexity:  Poly(n^1)
4.89/2.33	
4.89/2.33	   Cpx degree:  1
4.89/2.33	
4.89/2.33	   Solved cost: 5+3*n
4.89/2.33	
4.89/2.33	   Rule cost:   -4+3*A-3*B
4.89/2.33	
4.89/2.33	   Rule guard:  [ B>=0 && A>=3+B ]
4.89/2.33	
4.89/2.33	
4.89/2.33	
4.89/2.33	WORST_CASE(Omega(n^1),?)
4.89/2.33	
4.89/2.33	
4.89/2.33	----------------------------------------
4.89/2.33	
4.89/2.33	(4)
4.89/2.33	BOUNDS(n^1, INF)
4.91/2.36	EOF