5.63/2.52	WORST_CASE(Omega(n^2), O(n^2))
5.63/2.53	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.63/2.53	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.63/2.53	
5.63/2.53	
5.63/2.53	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.63/2.53	
5.63/2.53	(0) CpxIntTrs
5.63/2.53	(1) Koat Proof [FINISHED, 436 ms]
5.63/2.53	(2) BOUNDS(1, n^2)
5.63/2.53	(3) Loat Proof [FINISHED, 823 ms]
5.63/2.53	(4) BOUNDS(n^2, INF)
5.63/2.53	
5.63/2.53	
5.63/2.53	----------------------------------------
5.63/2.53	
5.63/2.53	(0)
5.63/2.53	Obligation:
5.63/2.53	Complexity Int TRS consisting of the following rules:
5.63/2.53	evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE
5.63/2.53	evalfentryin(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, 0)) :|: A >= 1 && B >= A + 1
5.63/2.53	evalfbb3in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: D >= B
5.63/2.53	evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: B >= D + 1
5.63/2.53	evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: 0 >= E + 1
5.63/2.53	evalfbb4in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: E >= 1
5.63/2.53	evalfbb4in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: TRUE
5.63/2.53	evalfbbin(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: A >= C + 1
5.63/2.53	evalfbbin(A, B, C, D) -> Com_1(evalfbb2in(A, B, C, D)) :|: C >= A
5.63/2.53	evalfbb1in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C + 1, D)) :|: TRUE
5.63/2.53	evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, 0, D + 1)) :|: TRUE
5.63/2.53	evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE
5.63/2.53	
5.63/2.53	The start-symbols are:[evalfstart_4]
5.63/2.53	
5.63/2.53	
5.63/2.53	----------------------------------------
5.63/2.53	
5.63/2.53	(1) Koat Proof (FINISHED)
5.63/2.53	YES(?, 20*ar_1 + 10*ar_0 + 20*ar_0*ar_1 + 16)
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Initial complexity problem:
5.63/2.53	
5.63/2.53	1:	T:
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.63/2.53	
5.63/2.53	2:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	A polynomial rank function with
5.63/2.53	
5.63/2.53		Pol(evalfstart) = 2
5.63/2.53	
5.63/2.53		Pol(evalfentryin) = 2
5.63/2.53	
5.63/2.53		Pol(evalfbb3in) = 2
5.63/2.53	
5.63/2.53		Pol(evalfreturnin) = 1
5.63/2.53	
5.63/2.53		Pol(evalfbb4in) = 2
5.63/2.53	
5.63/2.53		Pol(evalfbbin) = 2
5.63/2.53	
5.63/2.53		Pol(evalfbb1in) = 2
5.63/2.53	
5.63/2.53		Pol(evalfbb2in) = 2
5.63/2.53	
5.63/2.53		Pol(evalfstop) = 0
5.63/2.53	
5.63/2.53		Pol(koat_start) = 2
5.63/2.53	
5.63/2.53	orients all transitions weakly and the transitions
5.63/2.53	
5.63/2.53		evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53	strictly and produces the following problem:
5.63/2.53	
5.63/2.53	3:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3))
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1))
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.63/2.53	
5.63/2.53	  For symbol evalfbb1in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 2 >= 0 /\ X_1 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.63/2.53	
5.63/2.53	  For symbol evalfbb2in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 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
5.63/2.53	
5.63/2.53	  For symbol evalfbb3in: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.63/2.53	
5.63/2.53	  For symbol evalfbb4in: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.63/2.53	
5.63/2.53	  For symbol evalfbbin: X_2 - X_4 - 1 >= 0 /\ X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.63/2.53	
5.63/2.53	  For symbol evalfreturnin: X_4 >= 0 /\ X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 3 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 - 1 >= 0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	This yielded the following problem:
5.63/2.53	
5.63/2.53	4:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 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 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 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_0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	A polynomial rank function with
5.63/2.53	
5.63/2.53		Pol(koat_start) = 2*V_2
5.63/2.53	
5.63/2.53		Pol(evalfstart) = 2*V_2
5.63/2.53	
5.63/2.53		Pol(evalfreturnin) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfstop) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfbb2in) = 2*V_2 - 2*V_4 - 1
5.63/2.53	
5.63/2.53		Pol(evalfbb3in) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfbb1in) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfbbin) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfbb4in) = 2*V_2 - 2*V_4
5.63/2.53	
5.63/2.53		Pol(evalfentryin) = 2*V_2
5.63/2.53	
5.63/2.53	orients all transitions weakly and the transitions
5.63/2.53	
5.63/2.53		evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 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_0 ]
5.63/2.53	
5.63/2.53		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 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 ]
5.63/2.53	
5.63/2.53	strictly and produces the following problem:
5.63/2.53	
5.63/2.53	5:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)         evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 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 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)         evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 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_0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)         evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)         evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)         evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)         evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)         evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)         evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)         evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)         evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	A polynomial rank function with
5.63/2.53	
5.63/2.53		Pol(evalfbbin) = 2*V_1 - 2*V_3 + 1
5.63/2.53	
5.63/2.53		Pol(evalfbb1in) = 2*V_1 - 2*V_3
5.63/2.53	
5.63/2.53		Pol(evalfbb4in) = 2*V_1 - 2*V_3 + 1
5.63/2.53	
5.63/2.53		Pol(evalfbb3in) = 2*V_1 - 2*V_3 + 1
5.63/2.53	
5.63/2.53	and size complexities
5.63/2.53	
5.63/2.53		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.63/2.53	
5.63/2.53		S("evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.63/2.53	
5.63/2.53		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = 0
5.63/2.53	
5.63/2.53		S("evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = 0
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-2) = 0
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= ar_1 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_1 >= ar_3 + 1 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ 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 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ 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 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ 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 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ 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 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 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_0 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 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_0 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 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_0 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 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_0 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 - 2 >= 0 /\\ ar_0 - ar_2 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 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) = 0
5.63/2.53	
5.63/2.53		S("evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\\ ar_3 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 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 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 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
5.63/2.53	
5.63/2.53		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = ar_0
5.63/2.53	
5.63/2.53		S("evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\\ ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 3 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_1
5.63/2.53	
5.63/2.53		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.63/2.53	
5.63/2.53		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.63/2.53	
5.63/2.53		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.63/2.53	
5.63/2.53		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.63/2.53	
5.63/2.53	orients the transitions
5.63/2.53	
5.63/2.53		evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.63/2.53	
5.63/2.53		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53		evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53		evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53	weakly and the transitions
5.63/2.53	
5.63/2.53		evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53		evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53	strictly and produces the following problem:
5.63/2.53	
5.63/2.53	6:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)                                    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)                               evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 2*ar_1 + 1, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)                               evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 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_0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 2*ar_1 + 1, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)                                    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)                                    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: ?, Cost: 1)                                    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)                                    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)                                    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Repeatedly propagating knowledge in problem 6 produces the following problem:
5.63/2.53	
5.63/2.53	7:	T:
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 0)                                    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)                               evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 2*ar_1 + 1, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_0 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_1, Cost: 1)                               evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 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_0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 2*ar_1 + 1, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ 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 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 4*ar_1 + 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 4*ar_1 + 2, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2*ar_0 + 4*ar_0*ar_1 + 4*ar_1 + 2, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_1 >= ar_3 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 2, Cost: 1)                                    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 /\ ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 3 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= ar_1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)                                    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, 0, 0)) [ ar_0 >= 1 /\ ar_1 >= ar_0 + 1 ]
5.63/2.53	
5.63/2.53			(Comp: 1, Cost: 1)                                    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
5.63/2.53	
5.63/2.53		start location:	koat_start
5.63/2.53	
5.63/2.53		leaf cost:	0
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Complexity upper bound 20*ar_1 + 10*ar_0 + 20*ar_0*ar_1 + 16
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Time: 0.438 sec (SMT: 0.346 sec)
5.63/2.53	
5.63/2.53	
5.63/2.53	----------------------------------------
5.63/2.53	
5.63/2.53	(2)
5.63/2.53	BOUNDS(1, n^2)
5.63/2.53	
5.63/2.53	----------------------------------------
5.63/2.53	
5.63/2.53	(3) Loat Proof (FINISHED)
5.63/2.53	
5.63/2.53	
5.63/2.53	### Pre-processing the ITS problem ###
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Initial linear ITS problem
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	      0: evalfstart -> evalfentryin : [], cost: 1
5.63/2.53	
5.63/2.53	      1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
5.63/2.53	
5.63/2.53	      2: evalfbb3in -> evalfreturnin : [ D>=B ], cost: 1
5.63/2.53	
5.63/2.53	      3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1
5.63/2.53	
5.63/2.53	      4: evalfbb4in -> evalfbbin : [ 0>=1+free ], cost: 1
5.63/2.53	
5.63/2.53	      5: evalfbb4in -> evalfbbin : [ free_1>=1 ], cost: 1
5.63/2.53	
5.63/2.53	      6: evalfbb4in -> evalfreturnin : [], cost: 1
5.63/2.53	
5.63/2.53	      7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1
5.63/2.53	
5.63/2.53	      8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1
5.63/2.53	
5.63/2.53	      9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1
5.63/2.53	
5.63/2.53	     10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1
5.63/2.53	
5.63/2.53	     11: evalfreturnin -> evalfstop : [], cost: 1
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Removed unreachable and leaf rules:
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	      0: evalfstart -> evalfentryin : [], cost: 1
5.63/2.53	
5.63/2.53	      1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
5.63/2.53	
5.63/2.53	      3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1
5.63/2.53	
5.63/2.53	      4: evalfbb4in -> evalfbbin : [ 0>=1+free ], cost: 1
5.63/2.53	
5.63/2.53	      5: evalfbb4in -> evalfbbin : [ free_1>=1 ], cost: 1
5.63/2.53	
5.63/2.53	      7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1
5.63/2.53	
5.63/2.53	      8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1
5.63/2.53	
5.63/2.53	      9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1
5.63/2.53	
5.63/2.53	     10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Simplified all rules, resulting in:
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	      0: evalfstart -> evalfentryin : [], cost: 1
5.63/2.53	
5.63/2.53	      1: evalfentryin -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 1
5.63/2.53	
5.63/2.53	      3: evalfbb3in -> evalfbb4in : [ B>=1+D ], cost: 1
5.63/2.53	
5.63/2.53	      5: evalfbb4in -> evalfbbin : [], cost: 1
5.63/2.53	
5.63/2.53	      7: evalfbbin -> evalfbb1in : [ A>=1+C ], cost: 1
5.63/2.53	
5.63/2.53	      8: evalfbbin -> evalfbb2in : [ C>=A ], cost: 1
5.63/2.53	
5.63/2.53	      9: evalfbb1in -> evalfbb3in : C'=1+C, [], cost: 1
5.63/2.53	
5.63/2.53	     10: evalfbb2in -> evalfbb3in : C'=0, D'=1+D, [], cost: 1
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	### Simplification by acceleration and chaining ###
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Eliminated locations (on linear paths):
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2
5.63/2.53	
5.63/2.53	     13: evalfbb3in -> evalfbbin : [ B>=1+D ], cost: 2
5.63/2.53	
5.63/2.53	     14: evalfbbin -> evalfbb3in : C'=1+C, [ A>=1+C ], cost: 2
5.63/2.53	
5.63/2.53	     15: evalfbbin -> evalfbb3in : C'=0, D'=1+D, [ C>=A ], cost: 2
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Eliminated locations (on tree-shaped paths):
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2
5.63/2.53	
5.63/2.53	     16: evalfbb3in -> evalfbb3in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 4
5.63/2.53	
5.63/2.53	     17: evalfbb3in -> evalfbb3in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 4
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Accelerating simple loops of location 2.
5.63/2.53	
5.63/2.53	   Accelerating the following rules:
5.63/2.53	
5.63/2.53	     16: evalfbb3in -> evalfbb3in : C'=1+C, [ B>=1+D && A>=1+C ], cost: 4
5.63/2.53	
5.63/2.53	     17: evalfbb3in -> evalfbb3in : C'=0, D'=1+D, [ B>=1+D && C>=A ], cost: 4
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	   Accelerated rule 16 with metering function -C+A, yielding the new rule 18.
5.63/2.53	
5.63/2.53	   Accelerated rule 17 with metering function -D+B (after strengthening guard), yielding the new rule 19.
5.63/2.53	
5.63/2.53	   Nested simple loops 17 (outer loop) and 18 (inner loop) with metering function -1-D+B, resulting in the new rules: 20, 21.
5.63/2.53	
5.63/2.53	   Removing the simple loops: 16 17.
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Accelerated all simple loops using metering functions (where possible):
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2
5.63/2.53	
5.63/2.53	     18: evalfbb3in -> evalfbb3in : C'=A, [ B>=1+D && A>=1+C ], cost: -4*C+4*A
5.63/2.53	
5.63/2.53	     19: evalfbb3in -> evalfbb3in : C'=0, D'=B, [ B>=1+D && C>=A && 0>=A ], cost: -4*D+4*B
5.63/2.53	
5.63/2.53	     20: evalfbb3in -> evalfbb3in : C'=A, D'=-1+B, [ C>=A && B>=2+D && A>=1 ], cost: -4-4*(1+D-B)*A-4*D+4*B
5.63/2.53	
5.63/2.53	     21: evalfbb3in -> evalfbb3in : C'=A, D'=-1+B, [ A>=1+C && B>=2+D && A>=1 ], cost: -4-4*C-4*(1+D-B)*A-4*D+4*A+4*B
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Chained accelerated rules (with incoming rules):
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     12: evalfstart -> evalfbb3in : C'=0, D'=0, [ A>=1 && B>=1+A ], cost: 2
5.63/2.53	
5.63/2.53	     22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A
5.63/2.53	
5.63/2.53	     23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*(-1+B)*A+4*B
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Removed unreachable locations (and leaf rules with constant cost):
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A
5.63/2.53	
5.63/2.53	     23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*(-1+B)*A+4*B
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	### Computing asymptotic complexity ###
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Fully simplified ITS problem
5.63/2.53	
5.63/2.53	   Start location: evalfstart
5.63/2.53	
5.63/2.53	     22: evalfstart -> evalfbb3in : C'=A, D'=0, [ A>=1 && B>=1+A && B>=1 ], cost: 2+4*A
5.63/2.53	
5.63/2.53	     23: evalfstart -> evalfbb3in : C'=A, D'=-1+B, [ A>=1 && B>=1+A && B>=2 ], cost: -2+4*A+4*(-1+B)*A+4*B
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Computing asymptotic complexity for rule 22
5.63/2.53	
5.63/2.53	   Solved the limit problem by the following transformations:
5.63/2.53	
5.63/2.53	      Created initial limit problem:
5.63/2.53	
5.63/2.53	      2+4*A (+), A (+/+!), -A+B (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      removing all constraints (solved by SMT)
5.63/2.53	
5.63/2.53	      resulting limit problem: [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (C) using substitution {A==n,B==2*n}
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	   Solution:
5.63/2.53	
5.63/2.53	      A / n
5.63/2.53	
5.63/2.53	      B / 2*n
5.63/2.53	
5.63/2.53	   Resulting cost 2+4*n has complexity: Poly(n^1)
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Found new complexity Poly(n^1).
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Computing asymptotic complexity for rule 23
5.63/2.53	
5.63/2.53	   Solved the limit problem by the following transformations:
5.63/2.53	
5.63/2.53	      Created initial limit problem:
5.63/2.53	
5.63/2.53	      -2+4*A*B+4*B (+), A (+/+!), -A+B (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (C) using substitution {A==1}
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      1 (+/+!), -2+8*B (+), -1+B (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (C) using substitution {B==1+A}
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      1 (+/+!), 6+8*A (+), A (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (B), deleting 1 (+/+!)
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      6+8*A (+), A (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      removing all constraints (solved by SMT)
5.63/2.53	
5.63/2.53	      resulting limit problem: [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (C) using substitution {A==n}
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	   Solved the limit problem by the following transformations:
5.63/2.53	
5.63/2.53	      Created initial limit problem:
5.63/2.53	
5.63/2.53	      -2+4*A*B+4*B (+), A (+/+!), -A+B (+/+!) [not solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      removing all constraints (solved by SMT)
5.63/2.53	
5.63/2.53	      resulting limit problem: [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	      applying transformation rule (C) using substitution {A==1+n,B==2+n}
5.63/2.53	
5.63/2.53	      resulting limit problem:
5.63/2.53	
5.63/2.53	      [solved]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	   Solution:
5.63/2.53	
5.63/2.53	      A / 1+n
5.63/2.53	
5.63/2.53	      B / 2+n
5.63/2.53	
5.63/2.53	   Resulting cost 14+16*n+4*n^2 has complexity: Poly(n^2)
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Found new complexity Poly(n^2).
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	Obtained the following overall complexity (w.r.t. the length of the input n):
5.63/2.53	
5.63/2.53	   Complexity:  Poly(n^2)
5.63/2.53	
5.63/2.53	   Cpx degree:  2
5.63/2.53	
5.63/2.53	   Solved cost: 14+16*n+4*n^2
5.63/2.53	
5.63/2.53	   Rule cost:   -2+4*A+4*(-1+B)*A+4*B
5.63/2.53	
5.63/2.53	   Rule guard:  [ A>=1 && B>=1+A ]
5.63/2.53	
5.63/2.53	
5.63/2.53	
5.63/2.53	WORST_CASE(Omega(n^2),?)
5.63/2.53	
5.63/2.53	
5.63/2.53	----------------------------------------
5.63/2.53	
5.63/2.53	(4)
5.63/2.53	BOUNDS(n^2, INF)
5.63/2.55	EOF