5.58/2.89	WORST_CASE(Omega(n^1), O(n^2))
5.58/2.90	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.58/2.90	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.58/2.90	
5.58/2.90	
5.58/2.90	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2).
5.58/2.90	
5.58/2.90	(0) CpxIntTrs
5.58/2.90	(1) Koat Proof [FINISHED, 318 ms]
5.58/2.90	(2) BOUNDS(1, n^2)
5.58/2.90	(3) Loat Proof [FINISHED, 1219 ms]
5.58/2.90	(4) BOUNDS(n^1, INF)
5.58/2.90	
5.58/2.90	
5.58/2.90	----------------------------------------
5.58/2.90	
5.58/2.90	(0)
5.58/2.90	Obligation:
5.58/2.90	Complexity Int TRS consisting of the following rules:
5.58/2.90	evalEx7start(A, B, C) -> Com_1(evalEx7entryin(A, B, C)) :|: TRUE
5.58/2.90	evalEx7entryin(A, B, C) -> Com_1(evalEx7bb3in(A, B, A + 1)) :|: A >= 1 && B >= A + 1
5.58/2.90	evalEx7bb3in(A, B, C) -> Com_1(evalEx7bbin(A, B, C)) :|: A >= C + 1
5.58/2.90	evalEx7bb3in(A, B, C) -> Com_1(evalEx7bbin(A, B, C)) :|: C >= A + 1
5.58/2.90	evalEx7bb3in(A, B, C) -> Com_1(evalEx7returnin(A, B, C)) :|: C >= A && C <= A
5.58/2.90	evalEx7bbin(A, B, C) -> Com_1(evalEx7bb3in(A, B, 0)) :|: C >= B + 1
5.58/2.90	evalEx7bbin(A, B, C) -> Com_1(evalEx7bb3in(A, B, C + 1)) :|: B >= C
5.58/2.90	evalEx7returnin(A, B, C) -> Com_1(evalEx7stop(A, B, C)) :|: TRUE
5.58/2.90	
5.58/2.90	The start-symbols are:[evalEx7start_3]
5.58/2.90	
5.58/2.90	
5.58/2.90	----------------------------------------
5.58/2.90	
5.58/2.90	(1) Koat Proof (FINISHED)
5.58/2.90	YES(?, 20*ar_1^2 + 62*ar_1 + 35)
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Initial complexity problem:
5.58/2.90	
5.58/2.90	1:	T:
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.58/2.90	
5.58/2.90	2:	T:
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	A polynomial rank function with
5.58/2.90	
5.58/2.90		Pol(evalEx7start) = 2
5.58/2.90	
5.58/2.90		Pol(evalEx7entryin) = 2
5.58/2.90	
5.58/2.90		Pol(evalEx7bb3in) = 2
5.58/2.90	
5.58/2.90		Pol(evalEx7bbin) = 2
5.58/2.90	
5.58/2.90		Pol(evalEx7returnin) = 1
5.58/2.90	
5.58/2.90		Pol(evalEx7stop) = 0
5.58/2.90	
5.58/2.90		Pol(koat_start) = 2
5.58/2.90	
5.58/2.90	orients all transitions weakly and the transitions
5.58/2.90	
5.58/2.90		evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90		evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90	strictly and produces the following problem:
5.58/2.90	
5.58/2.90	3:	T:
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.58/2.90	
5.58/2.90	  For symbol evalEx7bb3in: X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.58/2.90	
5.58/2.90	  For symbol evalEx7bbin: X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.58/2.90	
5.58/2.90	  For symbol evalEx7returnin: X_2 - X_3 - 1 >= 0 /\ X_1 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ -X_1 + X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	This yielded the following problem:
5.58/2.90	
5.58/2.90	4:	T:
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7start(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7start(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
5.58/2.90	
5.58/2.90		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90	We thus obtain the following problem:
5.58/2.90	
5.58/2.90	5:	T:
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Testing for reachability in the complexity graph removes the following transition from problem 5:
5.58/2.90	
5.58/2.90		evalEx7start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2))
5.58/2.90	
5.58/2.90	We thus obtain the following problem:
5.58/2.90	
5.58/2.90	6:	T:
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	By chaining the transition evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 ] with all transitions in problem 6, the following new transition is obtained:
5.58/2.90	
5.58/2.90		evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90	We thus obtain the following problem:
5.58/2.90	
5.58/2.90	7:	T:
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 2)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	A polynomial rank function with
5.58/2.90	
5.58/2.90		Pol(evalEx7bbin) = V_2 - V_3 + 1
5.58/2.90	
5.58/2.90		Pol(evalEx7bb3in) = V_2 - V_3 + 1
5.58/2.90	
5.58/2.90	and size complexities
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-2) = 0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-2) = ?
5.58/2.90	
5.58/2.90	orients the transitions
5.58/2.90	
5.58/2.90		evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90		evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90	weakly and the transition
5.58/2.90	
5.58/2.90		evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90	strictly and produces the following problem:
5.58/2.90	
5.58/2.90	8:	T:
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 2)             evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)             evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)             evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)             evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 1, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 1)             evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)             evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Repeatedly propagating knowledge in problem 8 produces the following problem:
5.58/2.90	
5.58/2.90	9:	T:
5.58/2.90	
5.58/2.90			(Comp: ?, Cost: 2)             evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)             evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)             evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 2, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 1, Cost: 1)    evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 2, Cost: 1)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)             evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)             koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	A polynomial rank function with
5.58/2.90	
5.58/2.90		Pol(evalEx7bb3in) = V_2 - V_3 + 1
5.58/2.90	
5.58/2.90	and size complexities
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_0 + 1 ]", 0-2) = 3*ar_1 + 9
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_2 ]", 0-2) = 3*ar_1 + 9
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 >= ar_1 + 1 ]", 0-2) = 0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_2 = ar_0 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_0 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ?
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-0) = ar_0
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-1) = ar_1
5.58/2.90	
5.58/2.90		S("evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_0 >= ar_2 + 1 /\\ ar_1 >= ar_2 ]", 0-2) = ?
5.58/2.90	
5.58/2.90	orients the transitions
5.58/2.90	
5.58/2.90		evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90	weakly and the transition
5.58/2.90	
5.58/2.90		evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90	strictly and produces the following problem:
5.58/2.90	
5.58/2.90	10:	T:
5.58/2.90	
5.58/2.90			(Comp: 10*ar_1^2 + 28*ar_1 + 12, Cost: 2)    evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_0 >= ar_2 + 1 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)                           evalEx7returnin(ar_0, ar_1, ar_2) -> Com_1(evalEx7stop(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_0 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.58/2.90	
5.58/2.90			(Comp: 2, Cost: 1)                           evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7returnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 = ar_0 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 2, Cost: 1)                  evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, 0)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_1 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 1, Cost: 1)                  evalEx7bbin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_2 ]
5.58/2.90	
5.58/2.90			(Comp: 2*ar_1 + 2, Cost: 1)                  evalEx7bb3in(ar_0, ar_1, ar_2) -> Com_1(evalEx7bbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_2 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)                           evalEx7entryin(ar_0, ar_1, ar_2) -> Com_1(evalEx7bb3in(ar_0, ar_1, ar_0 + 1)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.58/2.90	
5.58/2.90			(Comp: 1, Cost: 1)                           koat_start(ar_0, ar_1, ar_2) -> Com_1(evalEx7entryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.58/2.90	
5.58/2.90		start location:	koat_start
5.58/2.90	
5.58/2.90		leaf cost:	0
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Complexity upper bound 20*ar_1^2 + 62*ar_1 + 35
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Time: 0.333 sec (SMT: 0.280 sec)
5.58/2.90	
5.58/2.90	
5.58/2.90	----------------------------------------
5.58/2.90	
5.58/2.90	(2)
5.58/2.90	BOUNDS(1, n^2)
5.58/2.90	
5.58/2.90	----------------------------------------
5.58/2.90	
5.58/2.90	(3) Loat Proof (FINISHED)
5.58/2.90	
5.58/2.90	
5.58/2.90	### Pre-processing the ITS problem ###
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Initial linear ITS problem
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      0: evalEx7start -> evalEx7entryin : [], cost: 1
5.58/2.90	
5.58/2.90	      1: evalEx7entryin -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 1
5.58/2.90	
5.58/2.90	      2: evalEx7bb3in -> evalEx7bbin : [ A>=1+C ], cost: 1
5.58/2.90	
5.58/2.90	      3: evalEx7bb3in -> evalEx7bbin : [ C>=1+A ], cost: 1
5.58/2.90	
5.58/2.90	      4: evalEx7bb3in -> evalEx7returnin : [ C==A ], cost: 1
5.58/2.90	
5.58/2.90	      5: evalEx7bbin -> evalEx7bb3in : C'=0, [ C>=1+B ], cost: 1
5.58/2.90	
5.58/2.90	      6: evalEx7bbin -> evalEx7bb3in : C'=1+C, [ B>=C ], cost: 1
5.58/2.90	
5.58/2.90	      7: evalEx7returnin -> evalEx7stop : [], cost: 1
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Removed unreachable and leaf rules:
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      0: evalEx7start -> evalEx7entryin : [], cost: 1
5.58/2.90	
5.58/2.90	      1: evalEx7entryin -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 1
5.58/2.90	
5.58/2.90	      2: evalEx7bb3in -> evalEx7bbin : [ A>=1+C ], cost: 1
5.58/2.90	
5.58/2.90	      3: evalEx7bb3in -> evalEx7bbin : [ C>=1+A ], cost: 1
5.58/2.90	
5.58/2.90	      5: evalEx7bbin -> evalEx7bb3in : C'=0, [ C>=1+B ], cost: 1
5.58/2.90	
5.58/2.90	      6: evalEx7bbin -> evalEx7bb3in : C'=1+C, [ B>=C ], cost: 1
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	### Simplification by acceleration and chaining ###
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Eliminated locations (on linear paths):
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      8: evalEx7start -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 2
5.58/2.90	
5.58/2.90	      2: evalEx7bb3in -> evalEx7bbin : [ A>=1+C ], cost: 1
5.58/2.90	
5.58/2.90	      3: evalEx7bb3in -> evalEx7bbin : [ C>=1+A ], cost: 1
5.58/2.90	
5.58/2.90	      5: evalEx7bbin -> evalEx7bb3in : C'=0, [ C>=1+B ], cost: 1
5.58/2.90	
5.58/2.90	      6: evalEx7bbin -> evalEx7bb3in : C'=1+C, [ B>=C ], cost: 1
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Eliminated locations (on tree-shaped paths):
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      8: evalEx7start -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 2
5.58/2.90	
5.58/2.90	      9: evalEx7bb3in -> evalEx7bb3in : C'=0, [ A>=1+C && C>=1+B ], cost: 2
5.58/2.90	
5.58/2.90	     10: evalEx7bb3in -> evalEx7bb3in : C'=1+C, [ A>=1+C && B>=C ], cost: 2
5.58/2.90	
5.58/2.90	     11: evalEx7bb3in -> evalEx7bb3in : C'=0, [ C>=1+A && C>=1+B ], cost: 2
5.58/2.90	
5.58/2.90	     12: evalEx7bb3in -> evalEx7bb3in : C'=1+C, [ C>=1+A && B>=C ], cost: 2
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Accelerating simple loops of location 2.
5.58/2.90	
5.58/2.90	   Accelerating the following rules:
5.58/2.90	
5.58/2.90	      9: evalEx7bb3in -> evalEx7bb3in : C'=0, [ A>=1+C && C>=1+B ], cost: 2
5.58/2.90	
5.58/2.90	     10: evalEx7bb3in -> evalEx7bb3in : C'=1+C, [ A>=1+C && B>=C ], cost: 2
5.58/2.90	
5.58/2.90	     11: evalEx7bb3in -> evalEx7bb3in : C'=0, [ C>=1+A && C>=1+B ], cost: 2
5.58/2.90	
5.58/2.90	     12: evalEx7bb3in -> evalEx7bb3in : C'=1+C, [ C>=1+A && B>=C ], cost: 2
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	   Accelerated rule 9 with NONTERM (after strengthening guard), yielding the new rule 13.
5.58/2.90	
5.58/2.90	   Accelerated rule 10 with backward acceleration, yielding the new rule 14.
5.58/2.90	
5.58/2.90	   Accelerated rule 10 with backward acceleration, yielding the new rule 15.
5.58/2.90	
5.58/2.90	   Accelerated rule 11 with NONTERM (after strengthening guard), yielding the new rule 16.
5.58/2.90	
5.58/2.90	   Accelerated rule 12 with metering function 1-C+B, yielding the new rule 17.
5.58/2.90	
5.58/2.90	   Nested simple loops 9 (outer loop) and 15 (inner loop) with NONTERM, resulting in the new rules: 18, 19.
5.58/2.90	
5.58/2.90	   Nested simple loops 11 (outer loop) and 17 (inner loop) with NONTERM, resulting in the new rules: 20, 21.
5.58/2.90	
5.58/2.90	   Removing the simple loops: 9 10 11 12.
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Accelerated all simple loops using metering functions (where possible):
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      8: evalEx7start -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 2
5.58/2.90	
5.58/2.90	     13: evalEx7bb3in -> [6] : [ A>=1+C && C>=1+B && A>=1 && 0>=1+B ], cost: INF
5.58/2.90	
5.58/2.90	     14: evalEx7bb3in -> evalEx7bb3in : C'=A, [ A>=1+C && B>=C && B>=-1+A ], cost: -2*C+2*A
5.58/2.90	
5.58/2.90	     15: evalEx7bb3in -> evalEx7bb3in : C'=1+B, [ A>=1+C && B>=C && A>=1+B ], cost: 2-2*C+2*B
5.58/2.90	
5.58/2.90	     16: evalEx7bb3in -> [6] : [ C>=1+A && C>=1+B && 0>=1+A && 0>=1+B ], cost: INF
5.58/2.90	
5.58/2.90	     17: evalEx7bb3in -> evalEx7bb3in : C'=1+B, [ C>=1+A && B>=C ], cost: 2-2*C+2*B
5.58/2.90	
5.58/2.90	     18: evalEx7bb3in -> [6] : [ A>=1+C && C>=1+B && A>=1 && B>=0 && A>=1+B && 4+2*B>=1 ], cost: INF
5.58/2.90	
5.58/2.90	     19: evalEx7bb3in -> [6] : C'=1+B, [ A>=1+C && B>=C && A>=2+B && A>=1 && B>=0 && 4+2*B>=1 ], cost: INF
5.58/2.90	
5.58/2.90	     20: evalEx7bb3in -> [6] : [ C>=1+A && C>=1+B && 0>=1+A && B>=0 && 4+2*B>=1 ], cost: INF
5.58/2.90	
5.58/2.90	     21: evalEx7bb3in -> [6] : C'=1+B, [ C>=1+A && B>=C && 1+B>=1+A && 0>=1+A && B>=0 && 4+2*B>=1 ], cost: INF
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Chained accelerated rules (with incoming rules):
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	      8: evalEx7start -> evalEx7bb3in : C'=1+A, [ A>=1 && B>=1+A ], cost: 2
5.58/2.90	
5.58/2.90	     22: evalEx7start -> evalEx7bb3in : C'=1+B, [ A>=1 && B>=1+A ], cost: 2-2*A+2*B
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Removed unreachable locations (and leaf rules with constant cost):
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	     22: evalEx7start -> evalEx7bb3in : C'=1+B, [ A>=1 && B>=1+A ], cost: 2-2*A+2*B
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	### Computing asymptotic complexity ###
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Fully simplified ITS problem
5.58/2.90	
5.58/2.90	   Start location: evalEx7start
5.58/2.90	
5.58/2.90	     22: evalEx7start -> evalEx7bb3in : C'=1+B, [ A>=1 && B>=1+A ], cost: 2-2*A+2*B
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	Computing asymptotic complexity for rule 22
5.58/2.90	
5.58/2.90	   Solved the limit problem by the following transformations:
5.58/2.90	
5.58/2.90	      Created initial limit problem:
5.58/2.90	
5.58/2.90	      2-2*A+2*B (+), A (+/+!), -A+B (+/+!) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (C) using substitution {A==1}
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      1 (+/+!), -1+B (+/+!), 2*B (+) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (C) using substitution {B==1+A}
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      1 (+/+!), A (+/+!), 2+2*A (+) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (B), deleting 1 (+/+!)
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      A (+/+!), 2+2*A (+) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (D), replacing 2+2*A (+) by 2*A (+)
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      2*A (+), A (+/+!) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (A), replacing 2*A (+) by A (+) and 2 (+!) using + limit vector (+,+!)
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      2 (+!), A (+) [not solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	      applying transformation rule (B), deleting 2 (+!)
5.58/2.90	
5.58/2.90	      resulting limit problem:
5.58/2.90	
5.58/2.90	      A (+) [solved]
5.58/2.90	
5.58/2.90	
5.58/2.90	
5.58/2.90	   Solution:
5.58/2.90	
5.58/2.90	      A / 1
5.58/2.90	
5.58/2.90	      B / 1+n
5.58/2.90	
5.58/2.90	   Resulting cost 2+2*n has complexity: Poly(n^1)
5.58/2.90	
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5.58/2.90	Found new complexity Poly(n^1).
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5.58/2.90	Obtained the following overall complexity (w.r.t. the length of the input n):
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5.58/2.90	   Complexity:  Poly(n^1)
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5.58/2.90	   Cpx degree:  1
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5.58/2.90	   Solved cost: 2+2*n
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5.58/2.90	   Rule cost:   2-2*A+2*B
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5.58/2.90	   Rule guard:  [ A>=1 && B>=1+A ]
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5.58/2.90	WORST_CASE(Omega(n^1),?)
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5.58/2.90	----------------------------------------
5.58/2.90	
5.58/2.90	(4)
5.58/2.90	BOUNDS(n^1, INF)
5.68/3.28	EOF