5.59/2.54	WORST_CASE(Omega(n^1), O(n^1))
5.59/2.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.59/2.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.59/2.55	
5.59/2.55	
5.59/2.55	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.59/2.55	
5.59/2.55	(0) CpxIntTrs
5.59/2.55	(1) Koat Proof [FINISHED, 402 ms]
5.59/2.55	(2) BOUNDS(1, n^1)
5.59/2.55	(3) Loat Proof [FINISHED, 803 ms]
5.59/2.55	(4) BOUNDS(n^1, INF)
5.59/2.55	
5.59/2.55	
5.59/2.55	----------------------------------------
5.59/2.55	
5.59/2.55	(0)
5.59/2.55	Obligation:
5.59/2.55	Complexity Int TRS consisting of the following rules:
5.59/2.55	evalEx4start(A, B, C, D) -> Com_1(evalEx4entryin(A, B, C, D)) :|: TRUE
5.59/2.55	evalEx4entryin(A, B, C, D) -> Com_1(evalEx4bb4in(1, A, C, D)) :|: TRUE
5.59/2.55	evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4bb2in(A, B, 0, B)) :|: A >= 1 && A <= 1
5.59/2.55	evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4returnin(A, B, C, D)) :|: 0 >= A
5.59/2.55	evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4returnin(A, B, C, D)) :|: A >= 2
5.59/2.55	evalEx4bb2in(A, B, C, D) -> Com_1(evalEx4bb4in(C, D, C, D)) :|: 0 >= D
5.59/2.55	evalEx4bb2in(A, B, C, D) -> Com_1(evalEx4bb3in(A, B, C, D)) :|: D >= 1
5.59/2.55	evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb1in(A, B, C, D)) :|: 0 >= E + 1
5.59/2.55	evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb1in(A, B, C, D)) :|: E >= 1
5.59/2.55	evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb4in(C, D, C, D)) :|: TRUE
5.59/2.55	evalEx4bb1in(A, B, C, D) -> Com_1(evalEx4bb2in(A, B, 1, D - 1)) :|: TRUE
5.59/2.55	evalEx4returnin(A, B, C, D) -> Com_1(evalEx4stop(A, B, C, D)) :|: TRUE
5.59/2.55	
5.59/2.55	The start-symbols are:[evalEx4start_4]
5.59/2.55	
5.59/2.55	
5.59/2.55	----------------------------------------
5.59/2.55	
5.59/2.55	(1) Koat Proof (FINISHED)
5.59/2.55	YES(?, 75*ar_0 + 42)
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Initial complexity problem:
5.59/2.55	
5.59/2.55	1:	T:
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.59/2.55	
5.59/2.55	2:	T:
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	A polynomial rank function with
5.59/2.55	
5.59/2.55		Pol(evalEx4start) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4entryin) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4bb4in) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4bb2in) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4returnin) = 1
5.59/2.55	
5.59/2.55		Pol(evalEx4bb3in) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4bb1in) = 2
5.59/2.55	
5.59/2.55		Pol(evalEx4stop) = 0
5.59/2.55	
5.59/2.55		Pol(koat_start) = 2
5.59/2.55	
5.59/2.55	orients all transitions weakly and the transitions
5.59/2.55	
5.59/2.55		evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55		evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55		evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55	strictly and produces the following problem:
5.59/2.55	
5.59/2.55	3:	T:
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.59/2.55	
5.59/2.55	  For symbol evalEx4bb1in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0
5.59/2.55	
5.59/2.55	  For symbol evalEx4bb2in: X_2 - X_4 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0
5.59/2.55	
5.59/2.55	  For symbol evalEx4bb3in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	This yielded the following problem:
5.59/2.55	
5.59/2.55	4:	T:
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	A polynomial rank function with
5.59/2.55	
5.59/2.55		Pol(koat_start) = 5*V_1 + 2
5.59/2.55	
5.59/2.55		Pol(evalEx4start) = 5*V_1 + 2
5.59/2.55	
5.59/2.55		Pol(evalEx4returnin) = 2*V_1 + 5*V_2
5.59/2.55	
5.59/2.55		Pol(evalEx4stop) = 2*V_1 + 5*V_2
5.59/2.55	
5.59/2.55		Pol(evalEx4bb1in) = 5*V_4
5.59/2.55	
5.59/2.55		Pol(evalEx4bb2in) = 2*V_1 + 2*V_3 + 5*V_4
5.59/2.55	
5.59/2.55		Pol(evalEx4bb3in) = 2*V_3 + 5*V_4 + 1
5.59/2.55	
5.59/2.55		Pol(evalEx4bb4in) = 2*V_1 + 5*V_2
5.59/2.55	
5.59/2.55		Pol(evalEx4entryin) = 5*V_1 + 2
5.59/2.55	
5.59/2.55	orients all transitions weakly and the transitions
5.59/2.55	
5.59/2.55		evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55		evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.59/2.55	
5.59/2.55		evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55		evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55		evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55	strictly and produces the following problem:
5.59/2.55	
5.59/2.55	5:	T:
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)             evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)             evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: ?, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)             evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)             evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	A polynomial rank function with
5.59/2.55	
5.59/2.55		Pol(evalEx4bb4in) = 2*V_1
5.59/2.55	
5.59/2.55		Pol(evalEx4bb2in) = 2*V_3 + 1
5.59/2.55	
5.59/2.55	and size complexities
5.59/2.55	
5.59/2.55		S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.59/2.55	
5.59/2.55		S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.59/2.55	
5.59/2.55		S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.59/2.55	
5.59/2.55		S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-2) = ar_2
5.59/2.55	
5.59/2.55		S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-3) = ar_3
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-2) = 0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 1
5.59/2.55	
5.59/2.55		S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_0
5.59/2.55	
5.59/2.55		S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 1
5.59/2.55	
5.59/2.55		S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_0
5.59/2.55	
5.59/2.55		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.59/2.55	
5.59/2.55		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.59/2.55	
5.59/2.55		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.59/2.55	
5.59/2.55		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.59/2.55	
5.59/2.55	orients the transitions
5.59/2.55	
5.59/2.55		evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55		evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55	weakly and the transitions
5.59/2.55	
5.59/2.55		evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55		evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55	strictly and produces the following problem:
5.59/2.55	
5.59/2.55	6:	T:
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)               evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]
5.59/2.55	
5.59/2.55			(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]
5.59/2.55	
5.59/2.55			(Comp: 25*ar_0 + 12, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)               evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]
5.59/2.55	
5.59/2.55			(Comp: 2, Cost: 1)               evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]
5.59/2.55	
5.59/2.55			(Comp: 25*ar_0 + 12, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)               evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))
5.59/2.55	
5.59/2.55			(Comp: 1, Cost: 1)               evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))
5.59/2.55	
5.59/2.55		start location:	koat_start
5.59/2.55	
5.59/2.55		leaf cost:	0
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Complexity upper bound 75*ar_0 + 42
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Time: 0.432 sec (SMT: 0.344 sec)
5.59/2.55	
5.59/2.55	
5.59/2.55	----------------------------------------
5.59/2.55	
5.59/2.55	(2)
5.59/2.55	BOUNDS(1, n^1)
5.59/2.55	
5.59/2.55	----------------------------------------
5.59/2.55	
5.59/2.55	(3) Loat Proof (FINISHED)
5.59/2.55	
5.59/2.55	
5.59/2.55	### Pre-processing the ITS problem ###
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Initial linear ITS problem
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	      0: evalEx4start -> evalEx4entryin : [], cost: 1
5.59/2.55	
5.59/2.55	      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      3: evalEx4bb4in -> evalEx4returnin : [ 0>=A ], cost: 1
5.59/2.55	
5.59/2.55	      4: evalEx4bb4in -> evalEx4returnin : [ A>=2 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      7: evalEx4bb3in -> evalEx4bb1in : [ 0>=1+free ], cost: 1
5.59/2.55	
5.59/2.55	      8: evalEx4bb3in -> evalEx4bb1in : [ free_1>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1
5.59/2.55	
5.59/2.55	     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1
5.59/2.55	
5.59/2.55	     11: evalEx4returnin -> evalEx4stop : [], cost: 1
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Removed unreachable and leaf rules:
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	      0: evalEx4start -> evalEx4entryin : [], cost: 1
5.59/2.55	
5.59/2.55	      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      7: evalEx4bb3in -> evalEx4bb1in : [ 0>=1+free ], cost: 1
5.59/2.55	
5.59/2.55	      8: evalEx4bb3in -> evalEx4bb1in : [ free_1>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1
5.59/2.55	
5.59/2.55	     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Simplified all rules, resulting in:
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	      0: evalEx4start -> evalEx4entryin : [], cost: 1
5.59/2.55	
5.59/2.55	      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      8: evalEx4bb3in -> evalEx4bb1in : [], cost: 1
5.59/2.55	
5.59/2.55	      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1
5.59/2.55	
5.59/2.55	     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	### Simplification by acceleration and chaining ###
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Eliminated locations (on linear paths):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1
5.59/2.55	
5.59/2.55	      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1
5.59/2.55	
5.59/2.55	     13: evalEx4bb3in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 2
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Eliminated locations (on tree-shaped paths):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2
5.59/2.55	
5.59/2.55	     15: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=-1+D, [ D>=1 ], cost: 3
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Accelerating simple loops of location 3.
5.59/2.55	
5.59/2.55	   Accelerating the following rules:
5.59/2.55	
5.59/2.55	     15: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=-1+D, [ D>=1 ], cost: 3
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	   Accelerated rule 15 with metering function D, yielding the new rule 16.
5.59/2.55	
5.59/2.55	   Removing the simple loops: 15.
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Accelerated all simple loops using metering functions (where possible):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2
5.59/2.55	
5.59/2.55	     16: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=0, [ D>=1 ], cost: 3*D
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Chained accelerated rules (with incoming rules):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1
5.59/2.55	
5.59/2.55	     17: evalEx4bb4in -> evalEx4bb2in : C'=1, D'=0, [ A==1 && B>=1 ], cost: 1+3*B
5.59/2.55	
5.59/2.55	      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1
5.59/2.55	
5.59/2.55	     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Eliminated locations (on tree-shaped paths):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	     18: evalEx4bb4in -> evalEx4bb4in : A'=0, B'=B, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2
5.59/2.55	
5.59/2.55	     19: evalEx4bb4in -> evalEx4bb4in : A'=0, B'=B, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3
5.59/2.55	
5.59/2.55	     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B
5.59/2.55	
5.59/2.55	     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Accelerating simple loops of location 2.
5.59/2.55	
5.59/2.55	   Simplified some of the simple loops (and removed duplicate rules).
5.59/2.55	
5.59/2.55	   Accelerating the following rules:
5.59/2.55	
5.59/2.55	     18: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2
5.59/2.55	
5.59/2.55	     19: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3
5.59/2.55	
5.59/2.55	     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	   Accelerated rule 18 with metering function A, yielding the new rule 22.
5.59/2.55	
5.59/2.55	   Accelerated rule 19 with metering function A, yielding the new rule 23.
5.59/2.55	
5.59/2.55	   Found no metering function for rule 20.
5.59/2.55	
5.59/2.55	   Removing the simple loops: 18 19.
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Accelerated all simple loops using metering functions (where possible):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B
5.59/2.55	
5.59/2.55	     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B
5.59/2.55	
5.59/2.55	     22: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2*A
5.59/2.55	
5.59/2.55	     23: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3*A
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Chained accelerated rules (with incoming rules):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2
5.59/2.55	
5.59/2.55	     24: evalEx4start -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A>=1 ], cost: 4+3*A
5.59/2.55	
5.59/2.55	     25: evalEx4start -> evalEx4bb4in : A'=0, B'=A, C'=0, D'=A, [ 0>=A ], cost: 4
5.59/2.55	
5.59/2.55	     26: evalEx4start -> evalEx4bb4in : A'=0, B'=A, C'=0, D'=A, [ A>=1 ], cost: 5
5.59/2.55	
5.59/2.55	     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Eliminated locations (on tree-shaped paths):
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     27: evalEx4start -> [9] : A'=1, B'=A, [ A>=1 ], cost: 3+3*A
5.59/2.55	
5.59/2.55	     28: evalEx4start -> [11] : [ A>=1 ], cost: 4+3*A
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	### Computing asymptotic complexity ###
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Fully simplified ITS problem
5.59/2.55	
5.59/2.55	   Start location: evalEx4start
5.59/2.55	
5.59/2.55	     28: evalEx4start -> [11] : [ A>=1 ], cost: 4+3*A
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Computing asymptotic complexity for rule 28
5.59/2.55	
5.59/2.55	   Solved the limit problem by the following transformations:
5.59/2.55	
5.59/2.55	      Created initial limit problem:
5.59/2.55	
5.59/2.55	      4+3*A (+), A (+/+!) [not solved]
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	      removing all constraints (solved by SMT)
5.59/2.55	
5.59/2.55	      resulting limit problem: [solved]
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	      applying transformation rule (C) using substitution {A==n}
5.59/2.55	
5.59/2.55	      resulting limit problem:
5.59/2.55	
5.59/2.55	      [solved]
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	   Solution:
5.59/2.55	
5.59/2.55	      A / n
5.59/2.55	
5.59/2.55	   Resulting cost 4+3*n has complexity: Poly(n^1)
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Found new complexity Poly(n^1).
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	Obtained the following overall complexity (w.r.t. the length of the input n):
5.59/2.55	
5.59/2.55	   Complexity:  Poly(n^1)
5.59/2.55	
5.59/2.55	   Cpx degree:  1
5.59/2.55	
5.59/2.55	   Solved cost: 4+3*n
5.59/2.55	
5.59/2.55	   Rule cost:   4+3*A
5.59/2.55	
5.59/2.55	   Rule guard:  [ A>=1 ]
5.59/2.55	
5.59/2.55	
5.59/2.55	
5.59/2.55	WORST_CASE(Omega(n^1),?)
5.59/2.55	
5.59/2.55	
5.59/2.55	----------------------------------------
5.59/2.55	
5.59/2.55	(4)
5.59/2.55	BOUNDS(n^1, INF)
5.59/2.57	EOF