5.40/2.36	WORST_CASE(Omega(n^1), O(n^1))
5.40/2.36	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.40/2.36	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.40/2.36	
5.40/2.36	
5.40/2.36	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.40/2.36	
5.40/2.36	(0) CpxIntTrs
5.40/2.36	(1) Koat Proof [FINISHED, 631 ms]
5.40/2.36	(2) BOUNDS(1, n^1)
5.40/2.36	(3) Loat Proof [FINISHED, 631 ms]
5.40/2.36	(4) BOUNDS(n^1, INF)
5.40/2.36	
5.40/2.36	
5.40/2.36	----------------------------------------
5.40/2.36	
5.40/2.36	(0)
5.40/2.36	Obligation:
5.40/2.36	Complexity Int TRS consisting of the following rules:
5.40/2.36	evalfstart(A, B, C) -> Com_1(evalfentryin(A, B, C)) :|: TRUE
5.40/2.36	evalfentryin(A, B, C) -> Com_1(evalfbb3in(C, B, A)) :|: A >= 1 && B >= A + 1
5.40/2.36	evalfbb3in(A, B, C) -> Com_1(evalfbbin(A, B, C)) :|: C >= 1 && B >= C + 1
5.40/2.36	evalfbb3in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: 0 >= C
5.40/2.36	evalfbb3in(A, B, C) -> Com_1(evalfreturnin(A, B, C)) :|: C >= B
5.40/2.36	evalfbbin(A, B, C) -> Com_1(evalfbb1in(A, B, C)) :|: A >= 1
5.40/2.36	evalfbbin(A, B, C) -> Com_1(evalfbb2in(A, B, C)) :|: 0 >= A
5.40/2.36	evalfbb1in(A, B, C) -> Com_1(evalfbb3in(A, B, C + 1)) :|: TRUE
5.40/2.36	evalfbb2in(A, B, C) -> Com_1(evalfbb3in(A, B, C - 1)) :|: TRUE
5.40/2.36	evalfreturnin(A, B, C) -> Com_1(evalfstop(A, B, C)) :|: TRUE
5.40/2.36	
5.40/2.36	The start-symbols are:[evalfstart_3]
5.40/2.36	
5.40/2.36	
5.40/2.36	----------------------------------------
5.40/2.36	
5.40/2.36	(1) Koat Proof (FINISHED)
5.40/2.36	YES(?, 3*ar_0 + 6*ar_1 + 15)
5.40/2.36	
5.40/2.36	
5.40/2.36	
5.40/2.36	Initial complexity problem:
5.40/2.36	
5.40/2.36	1:	T:
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1))
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1))
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
5.40/2.36	
5.40/2.36			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.36	
5.40/2.36		start location:	koat_start
5.40/2.36	
5.40/2.36		leaf cost:	0
5.40/2.36	
5.40/2.36	
5.40/2.36	
5.40/2.36	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.40/2.36	
5.40/2.36	2:	T:
5.40/2.36	
5.40/2.36			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.36	
5.40/2.36			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.36	
5.40/2.36			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1))
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1))
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	A polynomial rank function with
5.40/2.37	
5.40/2.37		Pol(evalfstart) = 2
5.40/2.37	
5.40/2.37		Pol(evalfentryin) = 2
5.40/2.37	
5.40/2.37		Pol(evalfbb3in) = 2
5.40/2.37	
5.40/2.37		Pol(evalfbbin) = 2
5.40/2.37	
5.40/2.37		Pol(evalfreturnin) = 1
5.40/2.37	
5.40/2.37		Pol(evalfbb1in) = 2
5.40/2.37	
5.40/2.37		Pol(evalfbb2in) = 2
5.40/2.37	
5.40/2.37		Pol(evalfstop) = 0
5.40/2.37	
5.40/2.37		Pol(koat_start) = 2
5.40/2.37	
5.40/2.37	orients all transitions weakly and the transitions
5.40/2.37	
5.40/2.37		evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37	strictly and produces the following problem:
5.40/2.37	
5.40/2.37	3:	T:
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1))
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1))
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.40/2.37	
5.40/2.37	  For symbol evalfbb1in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 2 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ X_1 - 1 >= 0
5.40/2.37	
5.40/2.37	  For symbol evalfbb2in: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ -X_1 >= 0
5.40/2.37	
5.40/2.37	  For symbol evalfbb3in: X_2 - 2 >= 0
5.40/2.37	
5.40/2.37	  For symbol evalfbbin: X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_2 - 2 >= 0
5.40/2.37	
5.40/2.37	  For symbol evalfreturnin: X_2 - 2 >= 0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	This yielded the following problem:
5.40/2.37	
5.40/2.37	4:	T:
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
5.40/2.37	
5.40/2.37		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	5:	T:
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Testing for reachability in the complexity graph removes the following transition from problem 5:
5.40/2.37	
5.40/2.37		evalfstart(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2))
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	6:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ] with all transitions in problem 6, the following new transition is obtained:
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	7:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ] with all transitions in problem 7, the following new transition is obtained:
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	8:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Testing for reachability in the complexity graph removes the following transition from problem 8:
5.40/2.37	
5.40/2.37		evalfreturnin(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	9:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 ] with all transitions in problem 9, the following new transition is obtained:
5.40/2.37	
5.40/2.37		evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	10:	T:
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Testing for reachability in the complexity graph removes the following transition from problem 10:
5.40/2.37	
5.40/2.37		evalfbb1in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	11:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 ] with all transitions in problem 11, the following new transition is obtained:
5.40/2.37	
5.40/2.37		evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	12:	T:
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Testing for reachability in the complexity graph removes the following transition from problem 12:
5.40/2.37	
5.40/2.37		evalfbb2in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	13:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ] with all transitions in problem 13, the following new transition is obtained:
5.40/2.37	
5.40/2.37		evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	14:	T:
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 14, the following new transition is obtained:
5.40/2.37	
5.40/2.37		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	15:	T:
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)    evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Testing for reachability in the complexity graph removes the following transition from problem 15:
5.40/2.37	
5.40/2.37		evalfentryin(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	16:	T:
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	By chaining the transition evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 ] with all transitions in problem 16, the following new transitions are obtained:
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37	We thus obtain the following problem:
5.40/2.37	
5.40/2.37	17:	T:
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Repeatedly propagating knowledge in problem 17 produces the following problem:
5.40/2.37	
5.40/2.37	18:	T:
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)    evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	A polynomial rank function with
5.40/2.37	
5.40/2.37		Pol(evalfbb3in) = V_2 - V_3
5.40/2.37	
5.40/2.37	and size complexities
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37	orients the transitions
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37	weakly and the transition
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37	strictly and produces the following problem:
5.40/2.37	
5.40/2.37	19:	T:
5.40/2.37	
5.40/2.37			(Comp: ?, Cost: 3)         evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2*ar_1, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)         evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)         evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)         evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)         evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	A polynomial rank function with
5.40/2.37	
5.40/2.37		Pol(evalfbb3in) = V_3
5.40/2.37	
5.40/2.37	and size complexities
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\\ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 /\\ ar_1 - 2 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_1 - 2 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ ar_2 >= ar_1 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\\ 0 >= ar_2 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 >= 1 /\\ ar_0 + ar_2 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-0) = ar_2
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-1) = ar_1
5.40/2.37	
5.40/2.37		S("evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\\ ar_2 >= 1 /\\ ar_1 >= ar_2 + 1 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ 0 >= ar_0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 >= 0 ]", 0-2) = ar_0
5.40/2.37	
5.40/2.37	orients the transitions
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37	weakly and the transition
5.40/2.37	
5.40/2.37		evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37	strictly and produces the following problem:
5.40/2.37	
5.40/2.37	20:	T:
5.40/2.37	
5.40/2.37			(Comp: ar_0, Cost: 3)      evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2*ar_1, Cost: 3)    evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - 2 >= 0 /\ ar_2 >= 1 /\ ar_1 >= ar_2 + 1 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)         evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ 0 >= ar_2 ]
5.40/2.37	
5.40/2.37			(Comp: 2, Cost: 2)         evalfbb3in(ar_0, ar_1, ar_2) -> Com_1(evalfstop(ar_0, ar_1, ar_2)) [ ar_1 - 2 >= 0 /\ ar_2 >= ar_1 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)         evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 - 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ 0 >= ar_0 /\ -ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ -ar_0 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 2)         evalfbbin(ar_0, ar_1, ar_2) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1)) [ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 >= 1 /\ ar_0 + ar_2 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ ar_0 - 1 >= 0 ]
5.40/2.37	
5.40/2.37			(Comp: 1, Cost: 3)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalfbbin(ar_2, ar_1, ar_0)) [ 0 <= 0 /\ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 /\ ar_1 - 2 >= 0 ]
5.40/2.37	
5.40/2.37		start location:	koat_start
5.40/2.37	
5.40/2.37		leaf cost:	0
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Complexity upper bound 3*ar_0 + 6*ar_1 + 15
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Time: 0.681 sec (SMT: 0.561 sec)
5.40/2.37	
5.40/2.37	
5.40/2.37	----------------------------------------
5.40/2.37	
5.40/2.37	(2)
5.40/2.37	BOUNDS(1, n^1)
5.40/2.37	
5.40/2.37	----------------------------------------
5.40/2.37	
5.40/2.37	(3) Loat Proof (FINISHED)
5.40/2.37	
5.40/2.37	
5.40/2.37	### Pre-processing the ITS problem ###
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Initial linear ITS problem
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	      0: evalfstart -> evalfentryin : [], cost: 1
5.40/2.37	
5.40/2.37	      1: evalfentryin -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 1
5.40/2.37	
5.40/2.37	      2: evalfbb3in -> evalfbbin : [ C>=1 && B>=1+C ], cost: 1
5.40/2.37	
5.40/2.37	      3: evalfbb3in -> evalfreturnin : [ 0>=C ], cost: 1
5.40/2.37	
5.40/2.37	      4: evalfbb3in -> evalfreturnin : [ C>=B ], cost: 1
5.40/2.37	
5.40/2.37	      5: evalfbbin -> evalfbb1in : [ A>=1 ], cost: 1
5.40/2.37	
5.40/2.37	      6: evalfbbin -> evalfbb2in : [ 0>=A ], cost: 1
5.40/2.37	
5.40/2.37	      7: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1
5.40/2.37	
5.40/2.37	      8: evalfbb2in -> evalfbb3in : C'=-1+C, [], cost: 1
5.40/2.37	
5.40/2.37	      9: evalfreturnin -> evalfstop : [], cost: 1
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Removed unreachable and leaf rules:
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	      0: evalfstart -> evalfentryin : [], cost: 1
5.40/2.37	
5.40/2.37	      1: evalfentryin -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 1
5.40/2.37	
5.40/2.37	      2: evalfbb3in -> evalfbbin : [ C>=1 && B>=1+C ], cost: 1
5.40/2.37	
5.40/2.37	      5: evalfbbin -> evalfbb1in : [ A>=1 ], cost: 1
5.40/2.37	
5.40/2.37	      6: evalfbbin -> evalfbb2in : [ 0>=A ], cost: 1
5.40/2.37	
5.40/2.37	      7: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1
5.40/2.37	
5.40/2.37	      8: evalfbb2in -> evalfbb3in : C'=-1+C, [], cost: 1
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	### Simplification by acceleration and chaining ###
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Eliminated locations (on linear paths):
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     10: evalfstart -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 2
5.40/2.37	
5.40/2.37	      2: evalfbb3in -> evalfbbin : [ C>=1 && B>=1+C ], cost: 1
5.40/2.37	
5.40/2.37	     11: evalfbbin -> evalfbb3in : C'=1+C, [ A>=1 ], cost: 2
5.40/2.37	
5.40/2.37	     12: evalfbbin -> evalfbb3in : C'=-1+C, [ 0>=A ], cost: 2
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Eliminated locations (on tree-shaped paths):
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     10: evalfstart -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 2
5.40/2.37	
5.40/2.37	     13: evalfbb3in -> evalfbb3in : C'=1+C, [ C>=1 && B>=1+C && A>=1 ], cost: 3
5.40/2.37	
5.40/2.37	     14: evalfbb3in -> evalfbb3in : C'=-1+C, [ C>=1 && B>=1+C && 0>=A ], cost: 3
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Accelerating simple loops of location 2.
5.40/2.37	
5.40/2.37	   Accelerating the following rules:
5.40/2.37	
5.40/2.37	     13: evalfbb3in -> evalfbb3in : C'=1+C, [ C>=1 && B>=1+C && A>=1 ], cost: 3
5.40/2.37	
5.40/2.37	     14: evalfbb3in -> evalfbb3in : C'=-1+C, [ C>=1 && B>=1+C && 0>=A ], cost: 3
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	   Accelerated rule 13 with metering function -C+B, yielding the new rule 15.
5.40/2.37	
5.40/2.37	   Accelerated rule 14 with metering function C, yielding the new rule 16.
5.40/2.37	
5.40/2.37	   Removing the simple loops: 13 14.
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Accelerated all simple loops using metering functions (where possible):
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     10: evalfstart -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 2
5.40/2.37	
5.40/2.37	     15: evalfbb3in -> evalfbb3in : C'=B, [ C>=1 && B>=1+C && A>=1 ], cost: -3*C+3*B
5.40/2.37	
5.40/2.37	     16: evalfbb3in -> evalfbb3in : C'=0, [ C>=1 && B>=1+C && 0>=A ], cost: 3*C
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Chained accelerated rules (with incoming rules):
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     10: evalfstart -> evalfbb3in : A'=C, C'=A, [ A>=1 && B>=1+A ], cost: 2
5.40/2.37	
5.40/2.37	     17: evalfstart -> evalfbb3in : A'=C, C'=B, [ A>=1 && B>=1+A && C>=1 ], cost: 2-3*A+3*B
5.40/2.37	
5.40/2.37	     18: evalfstart -> evalfbb3in : A'=C, C'=0, [ A>=1 && B>=1+A && 0>=C ], cost: 2+3*A
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Removed unreachable locations (and leaf rules with constant cost):
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     17: evalfstart -> evalfbb3in : A'=C, C'=B, [ A>=1 && B>=1+A && C>=1 ], cost: 2-3*A+3*B
5.40/2.37	
5.40/2.37	     18: evalfstart -> evalfbb3in : A'=C, C'=0, [ A>=1 && B>=1+A && 0>=C ], cost: 2+3*A
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	### Computing asymptotic complexity ###
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Fully simplified ITS problem
5.40/2.37	
5.40/2.37	   Start location: evalfstart
5.40/2.37	
5.40/2.37	     17: evalfstart -> evalfbb3in : A'=C, C'=B, [ A>=1 && B>=1+A && C>=1 ], cost: 2-3*A+3*B
5.40/2.37	
5.40/2.37	     18: evalfstart -> evalfbb3in : A'=C, C'=0, [ A>=1 && B>=1+A && 0>=C ], cost: 2+3*A
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Computing asymptotic complexity for rule 17
5.40/2.37	
5.40/2.37	   Solved the limit problem by the following transformations:
5.40/2.37	
5.40/2.37	      Created initial limit problem:
5.40/2.37	
5.40/2.37	      2-3*A+3*B (+), C (+/+!), A (+/+!), -A+B (+/+!) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (C) using substitution {A==1}
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      1 (+/+!), C (+/+!), -1+B (+/+!), -1+3*B (+) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (C) using substitution {B==1+A}
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      1 (+/+!), C (+/+!), A (+/+!), 2+3*A (+) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (C) using substitution {C==1}
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      1 (+/+!), A (+/+!), 2+3*A (+) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (B), deleting 1 (+/+!)
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      A (+/+!), 2+3*A (+) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (D), replacing 2+3*A (+) by 3*A (+)
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      3*A (+), A (+/+!) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (A), replacing 3*A (+) by A (+) and 3 (+!) using + limit vector (+,+!)
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      3 (+!), A (+) [not solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	      applying transformation rule (B), deleting 3 (+!)
5.40/2.37	
5.40/2.37	      resulting limit problem:
5.40/2.37	
5.40/2.37	      A (+) [solved]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	   Solution:
5.40/2.37	
5.40/2.37	      C / 1
5.40/2.37	
5.40/2.37	      A / 1
5.40/2.37	
5.40/2.37	      B / 1+n
5.40/2.37	
5.40/2.37	   Resulting cost 2+3*n has complexity: Poly(n^1)
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Found new complexity Poly(n^1).
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	Obtained the following overall complexity (w.r.t. the length of the input n):
5.40/2.37	
5.40/2.37	   Complexity:  Poly(n^1)
5.40/2.37	
5.40/2.37	   Cpx degree:  1
5.40/2.37	
5.40/2.37	   Solved cost: 2+3*n
5.40/2.37	
5.40/2.37	   Rule cost:   2-3*A+3*B
5.40/2.37	
5.40/2.37	   Rule guard:  [ A>=1 && B>=1+A && C>=1 ]
5.40/2.37	
5.40/2.37	
5.40/2.37	
5.40/2.37	WORST_CASE(Omega(n^1),?)
5.40/2.37	
5.40/2.37	
5.40/2.37	----------------------------------------
5.40/2.37	
5.40/2.37	(4)
5.40/2.37	BOUNDS(n^1, INF)
5.49/2.40	EOF