6.29/2.71	WORST_CASE(Omega(n^1), O(n^1))
6.29/2.72	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
6.29/2.72	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.29/2.72	
6.29/2.72	
6.29/2.72	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
6.29/2.72	
6.29/2.72	(0) CpxIntTrs
6.29/2.72	(1) Koat Proof [FINISHED, 541 ms]
6.29/2.72	(2) BOUNDS(1, n^1)
6.29/2.72	(3) Loat Proof [FINISHED, 1124 ms]
6.29/2.72	(4) BOUNDS(n^1, INF)
6.29/2.72	
6.29/2.72	
6.29/2.72	----------------------------------------
6.29/2.72	
6.29/2.72	(0)
6.29/2.72	Obligation:
6.29/2.72	Complexity Int TRS consisting of the following rules:
6.29/2.72	evalfstart(A, B, C, D) -> Com_1(evalfentryin(A, B, C, D)) :|: TRUE
6.29/2.72	evalfentryin(A, B, C, D) -> Com_1(evalfbb6in(0, B, C, D)) :|: TRUE
6.29/2.72	evalfbb6in(A, B, C, D) -> Com_1(evalfbbin(A, B, C, D)) :|: B >= A + 1
6.29/2.72	evalfbb6in(A, B, C, D) -> Com_1(evalfreturnin(A, B, C, D)) :|: A >= B
6.29/2.72	evalfbbin(A, B, C, D) -> Com_1(evalfbb2in(A, B, 0, A + 1)) :|: TRUE
6.29/2.72	evalfbb2in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: D >= B
6.29/2.72	evalfbb2in(A, B, C, D) -> Com_1(evalfbb3in(A, B, C, D)) :|: B >= D + 1
6.29/2.72	evalfbb3in(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: 0 >= E + 1
6.29/2.72	evalfbb3in(A, B, C, D) -> Com_1(evalfbb1in(A, B, C, D)) :|: E >= 1
6.29/2.72	evalfbb3in(A, B, C, D) -> Com_1(evalfbb4in(A, B, C, D)) :|: TRUE
6.29/2.72	evalfbb1in(A, B, C, D) -> Com_1(evalfbb2in(A, B, C + 1, D + 1)) :|: TRUE
6.29/2.72	evalfbb4in(A, B, C, D) -> Com_1(evalfbb6in(D - 1, B, C, D)) :|: C >= 1
6.29/2.72	evalfbb4in(A, B, C, D) -> Com_1(evalfbb6in(D, B, C, D)) :|: 0 >= C
6.29/2.72	evalfreturnin(A, B, C, D) -> Com_1(evalfstop(A, B, C, D)) :|: TRUE
6.29/2.72	
6.29/2.72	The start-symbols are:[evalfstart_4]
6.29/2.72	
6.29/2.72	
6.29/2.72	----------------------------------------
6.29/2.72	
6.29/2.72	(1) Koat Proof (FINISHED)
6.29/2.72	YES(?, 80*ar_1 + 6)
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Initial complexity problem:
6.29/2.72	
6.29/2.72	1:	T:
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(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 ]
6.29/2.72	
6.29/2.72		start location:	koat_start
6.29/2.72	
6.29/2.72		leaf cost:	0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Repeatedly propagating knowledge in problem 1 produces the following problem:
6.29/2.72	
6.29/2.72	2:	T:
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(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 ]
6.29/2.72	
6.29/2.72		start location:	koat_start
6.29/2.72	
6.29/2.72		leaf cost:	0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	A polynomial rank function with
6.29/2.72	
6.29/2.72		Pol(evalfstart) = 2
6.29/2.72	
6.29/2.72		Pol(evalfentryin) = 2
6.29/2.72	
6.29/2.72		Pol(evalfbb6in) = 2
6.29/2.72	
6.29/2.72		Pol(evalfbbin) = 2
6.29/2.72	
6.29/2.72		Pol(evalfreturnin) = 1
6.29/2.72	
6.29/2.72		Pol(evalfbb2in) = 2
6.29/2.72	
6.29/2.72		Pol(evalfbb4in) = 2
6.29/2.72	
6.29/2.72		Pol(evalfbb3in) = 2
6.29/2.72	
6.29/2.72		Pol(evalfbb1in) = 2
6.29/2.72	
6.29/2.72		Pol(evalfstop) = 0
6.29/2.72	
6.29/2.72		Pol(koat_start) = 2
6.29/2.72	
6.29/2.72	orients all transitions weakly and the transitions
6.29/2.72	
6.29/2.72		evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72		evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72	strictly and produces the following problem:
6.29/2.72	
6.29/2.72	3:	T:
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: 2, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1))
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72			(Comp: 2, Cost: 1)    evalfreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfstop(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(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 ]
6.29/2.72	
6.29/2.72		start location:	koat_start
6.29/2.72	
6.29/2.72		leaf cost:	0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Applied AI with 'oct' on problem 3 to obtain the following invariants:
6.29/2.72	
6.29/2.72	  For symbol evalfbb1in: X_2 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 2 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfbb2in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfbb3in: X_2 - X_4 - 1 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 3 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 2 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfbb4in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfbb6in: X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfbbin: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	  For symbol evalfreturnin: X_1 - X_2 >= 0 /\ X_1 >= 0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	This yielded the following problem:
6.29/2.72	
6.29/2.72	4:	T:
6.29/2.72	
6.29/2.72			(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 ]
6.29/2.72	
6.29/2.72			(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_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(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 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: 2, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: ?, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)    evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72		start location:	koat_start
6.29/2.72	
6.29/2.72		leaf cost:	0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	A polynomial rank function with
6.29/2.72	
6.29/2.72		Pol(koat_start) = 8*V_2
6.29/2.72	
6.29/2.72		Pol(evalfstart) = 8*V_2
6.29/2.72	
6.29/2.72		Pol(evalfreturnin) = -8*V_1 + 8*V_2
6.29/2.72	
6.29/2.72		Pol(evalfstop) = -8*V_1 + 8*V_2
6.29/2.72	
6.29/2.72		Pol(evalfbb4in) = 8*V_2 + 5*V_3 - 8*V_4 + 4
6.29/2.72	
6.29/2.72		Pol(evalfbb6in) = -8*V_1 + 8*V_2
6.29/2.72	
6.29/2.72		Pol(evalfbb1in) = 8*V_2 + 5*V_3 - 8*V_4 + 4
6.29/2.72	
6.29/2.72		Pol(evalfbb2in) = 8*V_2 + 5*V_3 - 8*V_4 + 6
6.29/2.72	
6.29/2.72		Pol(evalfbb3in) = 8*V_2 + 5*V_3 - 8*V_4 + 5
6.29/2.72	
6.29/2.72		Pol(evalfbbin) = -8*V_1 + 8*V_2 - 1
6.29/2.72	
6.29/2.72		Pol(evalfentryin) = 8*V_2
6.29/2.72	
6.29/2.72	orients all transitions weakly and the transitions
6.29/2.72	
6.29/2.72		evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72		evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72		evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72		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 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72		evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.29/2.72	
6.29/2.72		evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72		evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72		evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72	strictly and produces the following problem:
6.29/2.72	
6.29/2.72	5:	T:
6.29/2.72	
6.29/2.72			(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 ]
6.29/2.72	
6.29/2.72			(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_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ 0 >= ar_2 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(ar_3 - 1, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, ar_2 + 1, ar_3 + 1)) [ ar_1 - ar_3 - 1 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, 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 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb3in(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 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 3 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 2 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_3 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb2in(ar_0, ar_1, 0, ar_0 + 1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.29/2.72	
6.29/2.72			(Comp: 2, Cost: 1)         evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ]
6.29/2.72	
6.29/2.72			(Comp: 8*ar_1, Cost: 1)    evalfbb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)         evalfentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfbb6in(0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72			(Comp: 1, Cost: 1)         evalfstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfentryin(ar_0, ar_1, ar_2, ar_3))
6.29/2.72	
6.29/2.72		start location:	koat_start
6.29/2.72	
6.29/2.72		leaf cost:	0
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Complexity upper bound 80*ar_1 + 6
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Time: 0.519 sec (SMT: 0.416 sec)
6.29/2.72	
6.29/2.72	
6.29/2.72	----------------------------------------
6.29/2.72	
6.29/2.72	(2)
6.29/2.72	BOUNDS(1, n^1)
6.29/2.72	
6.29/2.72	----------------------------------------
6.29/2.72	
6.29/2.72	(3) Loat Proof (FINISHED)
6.29/2.72	
6.29/2.72	
6.29/2.72	### Pre-processing the ITS problem ###
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Initial linear ITS problem
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	      0: evalfstart -> evalfentryin : [], cost: 1
6.29/2.72	
6.29/2.72	      1: evalfentryin -> evalfbb6in : A'=0, [], cost: 1
6.29/2.72	
6.29/2.72	      2: evalfbb6in -> evalfbbin : [ B>=1+A ], cost: 1
6.29/2.72	
6.29/2.72	      3: evalfbb6in -> evalfreturnin : [ A>=B ], cost: 1
6.29/2.72	
6.29/2.72	      4: evalfbbin -> evalfbb2in : C'=0, D'=1+A, [], cost: 1
6.29/2.72	
6.29/2.72	      5: evalfbb2in -> evalfbb4in : [ D>=B ], cost: 1
6.29/2.72	
6.29/2.72	      6: evalfbb2in -> evalfbb3in : [ B>=1+D ], cost: 1
6.29/2.72	
6.29/2.72	      7: evalfbb3in -> evalfbb1in : [ 0>=1+free ], cost: 1
6.29/2.72	
6.29/2.72	      8: evalfbb3in -> evalfbb1in : [ free_1>=1 ], cost: 1
6.29/2.72	
6.29/2.72	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.29/2.72	
6.29/2.72	     10: evalfbb1in -> evalfbb2in : C'=1+C, D'=1+D, [], cost: 1
6.29/2.72	
6.29/2.72	     11: evalfbb4in -> evalfbb6in : A'=-1+D, [ C>=1 ], cost: 1
6.29/2.72	
6.29/2.72	     12: evalfbb4in -> evalfbb6in : A'=D, [ 0>=C ], cost: 1
6.29/2.72	
6.29/2.72	     13: evalfreturnin -> evalfstop : [], cost: 1
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Removed unreachable and leaf rules:
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	      0: evalfstart -> evalfentryin : [], cost: 1
6.29/2.72	
6.29/2.72	      1: evalfentryin -> evalfbb6in : A'=0, [], cost: 1
6.29/2.72	
6.29/2.72	      2: evalfbb6in -> evalfbbin : [ B>=1+A ], cost: 1
6.29/2.72	
6.29/2.72	      4: evalfbbin -> evalfbb2in : C'=0, D'=1+A, [], cost: 1
6.29/2.72	
6.29/2.72	      5: evalfbb2in -> evalfbb4in : [ D>=B ], cost: 1
6.29/2.72	
6.29/2.72	      6: evalfbb2in -> evalfbb3in : [ B>=1+D ], cost: 1
6.29/2.72	
6.29/2.72	      7: evalfbb3in -> evalfbb1in : [ 0>=1+free ], cost: 1
6.29/2.72	
6.29/2.72	      8: evalfbb3in -> evalfbb1in : [ free_1>=1 ], cost: 1
6.29/2.72	
6.29/2.72	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.29/2.72	
6.29/2.72	     10: evalfbb1in -> evalfbb2in : C'=1+C, D'=1+D, [], cost: 1
6.29/2.72	
6.29/2.72	     11: evalfbb4in -> evalfbb6in : A'=-1+D, [ C>=1 ], cost: 1
6.29/2.72	
6.29/2.72	     12: evalfbb4in -> evalfbb6in : A'=D, [ 0>=C ], cost: 1
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Simplified all rules, resulting in:
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	      0: evalfstart -> evalfentryin : [], cost: 1
6.29/2.72	
6.29/2.72	      1: evalfentryin -> evalfbb6in : A'=0, [], cost: 1
6.29/2.72	
6.29/2.72	      2: evalfbb6in -> evalfbbin : [ B>=1+A ], cost: 1
6.29/2.72	
6.29/2.72	      4: evalfbbin -> evalfbb2in : C'=0, D'=1+A, [], cost: 1
6.29/2.72	
6.29/2.72	      5: evalfbb2in -> evalfbb4in : [ D>=B ], cost: 1
6.29/2.72	
6.29/2.72	      6: evalfbb2in -> evalfbb3in : [ B>=1+D ], cost: 1
6.29/2.72	
6.29/2.72	      8: evalfbb3in -> evalfbb1in : [], cost: 1
6.29/2.72	
6.29/2.72	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.29/2.72	
6.29/2.72	     10: evalfbb1in -> evalfbb2in : C'=1+C, D'=1+D, [], cost: 1
6.29/2.72	
6.29/2.72	     11: evalfbb4in -> evalfbb6in : A'=-1+D, [ C>=1 ], cost: 1
6.29/2.72	
6.29/2.72	     12: evalfbb4in -> evalfbb6in : A'=D, [ 0>=C ], cost: 1
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	### Simplification by acceleration and chaining ###
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Eliminated locations (on linear paths):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     15: evalfbb6in -> evalfbb2in : C'=0, D'=1+A, [ B>=1+A ], cost: 2
6.29/2.72	
6.29/2.72	      5: evalfbb2in -> evalfbb4in : [ D>=B ], cost: 1
6.29/2.72	
6.29/2.72	      6: evalfbb2in -> evalfbb3in : [ B>=1+D ], cost: 1
6.29/2.72	
6.29/2.72	      9: evalfbb3in -> evalfbb4in : [], cost: 1
6.29/2.72	
6.29/2.72	     16: evalfbb3in -> evalfbb2in : C'=1+C, D'=1+D, [], cost: 2
6.29/2.72	
6.29/2.72	     11: evalfbb4in -> evalfbb6in : A'=-1+D, [ C>=1 ], cost: 1
6.29/2.72	
6.29/2.72	     12: evalfbb4in -> evalfbb6in : A'=D, [ 0>=C ], cost: 1
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Eliminated locations (on tree-shaped paths):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     15: evalfbb6in -> evalfbb2in : C'=0, D'=1+A, [ B>=1+A ], cost: 2
6.29/2.72	
6.29/2.72	     18: evalfbb2in -> evalfbb2in : C'=1+C, D'=1+D, [ B>=1+D ], cost: 3
6.29/2.72	
6.29/2.72	     19: evalfbb2in -> evalfbb6in : A'=-1+D, [ D>=B && C>=1 ], cost: 2
6.29/2.72	
6.29/2.72	     20: evalfbb2in -> evalfbb6in : A'=D, [ D>=B && 0>=C ], cost: 2
6.29/2.72	
6.29/2.72	     21: evalfbb2in -> evalfbb6in : A'=-1+D, [ B>=1+D && C>=1 ], cost: 3
6.29/2.72	
6.29/2.72	     22: evalfbb2in -> evalfbb6in : A'=D, [ B>=1+D && 0>=C ], cost: 3
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Accelerating simple loops of location 4.
6.29/2.72	
6.29/2.72	   Accelerating the following rules:
6.29/2.72	
6.29/2.72	     18: evalfbb2in -> evalfbb2in : C'=1+C, D'=1+D, [ B>=1+D ], cost: 3
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	   Accelerated rule 18 with metering function -D+B, yielding the new rule 23.
6.29/2.72	
6.29/2.72	   Removing the simple loops: 18.
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Accelerated all simple loops using metering functions (where possible):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     15: evalfbb6in -> evalfbb2in : C'=0, D'=1+A, [ B>=1+A ], cost: 2
6.29/2.72	
6.29/2.72	     19: evalfbb2in -> evalfbb6in : A'=-1+D, [ D>=B && C>=1 ], cost: 2
6.29/2.72	
6.29/2.72	     20: evalfbb2in -> evalfbb6in : A'=D, [ D>=B && 0>=C ], cost: 2
6.29/2.72	
6.29/2.72	     21: evalfbb2in -> evalfbb6in : A'=-1+D, [ B>=1+D && C>=1 ], cost: 3
6.29/2.72	
6.29/2.72	     22: evalfbb2in -> evalfbb6in : A'=D, [ B>=1+D && 0>=C ], cost: 3
6.29/2.72	
6.29/2.72	     23: evalfbb2in -> evalfbb2in : C'=C-D+B, D'=B, [ B>=1+D ], cost: -3*D+3*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Chained accelerated rules (with incoming rules):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     15: evalfbb6in -> evalfbb2in : C'=0, D'=1+A, [ B>=1+A ], cost: 2
6.29/2.72	
6.29/2.72	     24: evalfbb6in -> evalfbb2in : C'=-1-A+B, D'=B, [ B>=2+A ], cost: -1-3*A+3*B
6.29/2.72	
6.29/2.72	     19: evalfbb2in -> evalfbb6in : A'=-1+D, [ D>=B && C>=1 ], cost: 2
6.29/2.72	
6.29/2.72	     20: evalfbb2in -> evalfbb6in : A'=D, [ D>=B && 0>=C ], cost: 2
6.29/2.72	
6.29/2.72	     21: evalfbb2in -> evalfbb6in : A'=-1+D, [ B>=1+D && C>=1 ], cost: 3
6.29/2.72	
6.29/2.72	     22: evalfbb2in -> evalfbb6in : A'=D, [ B>=1+D && 0>=C ], cost: 3
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Eliminated locations (on tree-shaped paths):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     25: evalfbb6in -> evalfbb6in : A'=1+A, C'=0, D'=1+A, [ B>=1+A && 1+A>=B ], cost: 4
6.29/2.72	
6.29/2.72	     26: evalfbb6in -> evalfbb6in : A'=1+A, C'=0, D'=1+A, [ B>=2+A ], cost: 5
6.29/2.72	
6.29/2.72	     27: evalfbb6in -> evalfbb6in : A'=-1+B, C'=-1-A+B, D'=B, [ B>=2+A ], cost: 1-3*A+3*B
6.29/2.72	
6.29/2.72	     28: evalfbb6in -> [11] : [ B>=2+A ], cost: -1-3*A+3*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Accelerating simple loops of location 2.
6.29/2.72	
6.29/2.72	   Simplified some of the simple loops (and removed duplicate rules).
6.29/2.72	
6.29/2.72	   Accelerating the following rules:
6.29/2.72	
6.29/2.72	     25: evalfbb6in -> evalfbb6in : A'=1+A, C'=0, D'=1+A, [ 1+A-B==0 ], cost: 4
6.29/2.72	
6.29/2.72	     26: evalfbb6in -> evalfbb6in : A'=1+A, C'=0, D'=1+A, [ B>=2+A ], cost: 5
6.29/2.72	
6.29/2.72	     27: evalfbb6in -> evalfbb6in : A'=-1+B, C'=-1-A+B, D'=B, [ B>=2+A ], cost: 1-3*A+3*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	   Accelerated rule 25 with metering function -A+B, yielding the new rule 29.
6.29/2.72	
6.29/2.72	   Accelerated rule 26 with metering function -1-A+B, yielding the new rule 30.
6.29/2.72	
6.29/2.72	   Found no metering function for rule 27.
6.29/2.72	
6.29/2.72	   Removing the simple loops: 25 26.
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Accelerated all simple loops using metering functions (where possible):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     27: evalfbb6in -> evalfbb6in : A'=-1+B, C'=-1-A+B, D'=B, [ B>=2+A ], cost: 1-3*A+3*B
6.29/2.72	
6.29/2.72	     28: evalfbb6in -> [11] : [ B>=2+A ], cost: -1-3*A+3*B
6.29/2.72	
6.29/2.72	     29: evalfbb6in -> evalfbb6in : A'=B, C'=0, D'=B, [ 1+A-B==0 ], cost: -4*A+4*B
6.29/2.72	
6.29/2.72	     30: evalfbb6in -> evalfbb6in : A'=-1+B, C'=0, D'=-1+B, [ B>=2+A ], cost: -5-5*A+5*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Chained accelerated rules (with incoming rules):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     14: evalfstart -> evalfbb6in : A'=0, [], cost: 2
6.29/2.72	
6.29/2.72	     31: evalfstart -> evalfbb6in : A'=-1+B, C'=-1+B, D'=B, [ B>=2 ], cost: 3+3*B
6.29/2.72	
6.29/2.72	     32: evalfstart -> evalfbb6in : A'=B, C'=0, D'=B, [ 1-B==0 ], cost: 2+4*B
6.29/2.72	
6.29/2.72	     33: evalfstart -> evalfbb6in : A'=-1+B, C'=0, D'=-1+B, [ B>=2 ], cost: -3+5*B
6.29/2.72	
6.29/2.72	     28: evalfbb6in -> [11] : [ B>=2+A ], cost: -1-3*A+3*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Eliminated locations (on tree-shaped paths):
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     34: evalfstart -> [11] : A'=0, [ B>=2 ], cost: 1+3*B
6.29/2.72	
6.29/2.72	     35: evalfstart -> [13] : [ B>=2 ], cost: 3+3*B
6.29/2.72	
6.29/2.72	     36: evalfstart -> [13] : [ 1-B==0 ], cost: 2+4*B
6.29/2.72	
6.29/2.72	     37: evalfstart -> [13] : [ B>=2 ], cost: -3+5*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	### Computing asymptotic complexity ###
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Fully simplified ITS problem
6.29/2.72	
6.29/2.72	   Start location: evalfstart
6.29/2.72	
6.29/2.72	     35: evalfstart -> [13] : [ B>=2 ], cost: 3+3*B
6.29/2.72	
6.29/2.72	     36: evalfstart -> [13] : [ 1-B==0 ], cost: 2+4*B
6.29/2.72	
6.29/2.72	     37: evalfstart -> [13] : [ B>=2 ], cost: -3+5*B
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Computing asymptotic complexity for rule 35
6.29/2.72	
6.29/2.72	   Solved the limit problem by the following transformations:
6.29/2.72	
6.29/2.72	      Created initial limit problem:
6.29/2.72	
6.29/2.72	      3+3*B (+), -1+B (+/+!) [not solved]
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	      removing all constraints (solved by SMT)
6.29/2.72	
6.29/2.72	      resulting limit problem: [solved]
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	      applying transformation rule (C) using substitution {B==n}
6.29/2.72	
6.29/2.72	      resulting limit problem:
6.29/2.72	
6.29/2.72	      [solved]
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	   Solution:
6.29/2.72	
6.29/2.72	      B / n
6.29/2.72	
6.29/2.72	   Resulting cost 3+3*n has complexity: Poly(n^1)
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Found new complexity Poly(n^1).
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	Obtained the following overall complexity (w.r.t. the length of the input n):
6.29/2.72	
6.29/2.72	   Complexity:  Poly(n^1)
6.29/2.72	
6.29/2.72	   Cpx degree:  1
6.29/2.72	
6.29/2.72	   Solved cost: 3+3*n
6.29/2.72	
6.29/2.72	   Rule cost:   3+3*B
6.29/2.72	
6.29/2.72	   Rule guard:  [ B>=2 ]
6.29/2.72	
6.29/2.72	
6.29/2.72	
6.29/2.72	WORST_CASE(Omega(n^1),?)
6.29/2.72	
6.29/2.72	
6.29/2.72	----------------------------------------
6.29/2.72	
6.29/2.72	(4)
6.29/2.72	BOUNDS(n^1, INF)
6.29/2.75	EOF