6.16/2.69	WORST_CASE(Omega(n^2), O(n^2))
6.16/2.70	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
6.16/2.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
6.16/2.70	
6.16/2.70	
6.16/2.70	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
6.16/2.70	
6.16/2.70	(0) CpxIntTrs
6.16/2.70	(1) Koat Proof [FINISHED, 505 ms]
6.16/2.70	(2) BOUNDS(1, n^2)
6.16/2.70	(3) Loat Proof [FINISHED, 1021 ms]
6.16/2.70	(4) BOUNDS(n^2, INF)
6.16/2.70	
6.16/2.70	
6.16/2.70	----------------------------------------
6.16/2.70	
6.16/2.70	(0)
6.16/2.70	Obligation:
6.16/2.70	Complexity Int TRS consisting of the following rules:
6.16/2.70	evalEx1start(A, B, C, D) -> Com_1(evalEx1entryin(A, B, C, D)) :|: TRUE
6.16/2.70	evalEx1entryin(A, B, C, D) -> Com_1(evalEx1bb6in(0, A, C, D)) :|: TRUE
6.16/2.70	evalEx1bb6in(A, B, C, D) -> Com_1(evalEx1bbin(A, B, C, D)) :|: B >= A + 1
6.16/2.70	evalEx1bb6in(A, B, C, D) -> Com_1(evalEx1returnin(A, B, C, D)) :|: A >= B
6.16/2.70	evalEx1bbin(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, A + 1, B)) :|: TRUE
6.16/2.70	evalEx1bb4in(A, B, C, D) -> Com_1(evalEx1bb1in(A, B, C, D)) :|: D >= C + 1
6.16/2.70	evalEx1bb4in(A, B, C, D) -> Com_1(evalEx1bb5in(A, B, C, D)) :|: C >= D
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C, D - 1)) :|: 0 >= E + 1
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C, D - 1)) :|: 0 >= E + 1 && E >= 1
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C, D - 1)) :|: E >= 1
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C, D)) :|: 0 >= 1
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C + 1, D - 1)) :|: 0 >= 1
6.16/2.70	evalEx1bb1in(A, B, C, D) -> Com_1(evalEx1bb4in(A, B, C + 1, D)) :|: TRUE
6.16/2.70	evalEx1bb5in(A, B, C, D) -> Com_1(evalEx1bb6in(A + 1, D, C, D)) :|: TRUE
6.16/2.70	evalEx1returnin(A, B, C, D) -> Com_1(evalEx1stop(A, B, C, D)) :|: TRUE
6.16/2.70	
6.16/2.70	The start-symbols are:[evalEx1start_4]
6.16/2.70	
6.16/2.70	
6.16/2.70	----------------------------------------
6.16/2.70	
6.16/2.70	(1) Koat Proof (FINISHED)
6.16/2.70	YES(?, 22*ar_0 + 24*ar_0^2 + 14)
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Initial complexity problem:
6.16/2.70	
6.16/2.70	1:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 /\ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3 - 1)) [ 0 >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Testing for reachability in the complexity graph removes the following transitions from problem 1:
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 /\ e >= 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3 - 1)) [ 0 >= 1 ]
6.16/2.70	
6.16/2.70	We thus obtain the following problem:
6.16/2.70	
6.16/2.70	2:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Repeatedly propagating knowledge in problem 2 produces the following problem:
6.16/2.70	
6.16/2.70	3:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)    evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)    evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	A polynomial rank function with
6.16/2.70	
6.16/2.70		Pol(evalEx1bb5in) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb6in) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb1in) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb4in) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1returnin) = 1
6.16/2.70	
6.16/2.70		Pol(evalEx1stop) = 0
6.16/2.70	
6.16/2.70		Pol(evalEx1bbin) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1entryin) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1start) = 2
6.16/2.70	
6.16/2.70		Pol(koat_start) = 2
6.16/2.70	
6.16/2.70	orients all transitions weakly and the transitions
6.16/2.70	
6.16/2.70		evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70		evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70	strictly and produces the following problem:
6.16/2.70	
6.16/2.70	4:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)    evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)    evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)    evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	A polynomial rank function with
6.16/2.70	
6.16/2.70		Pol(evalEx1bb5in) = -V_1 + V_4
6.16/2.70	
6.16/2.70		Pol(evalEx1bb6in) = -V_1 + V_2 + 1
6.16/2.70	
6.16/2.70		Pol(evalEx1bb1in) = -V_1 + V_4
6.16/2.70	
6.16/2.70		Pol(evalEx1bb4in) = -V_1 + V_4
6.16/2.70	
6.16/2.70		Pol(evalEx1returnin) = -V_1 + V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1stop) = -V_1 + V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1bbin) = -V_1 + V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1entryin) = V_1 + 1
6.16/2.70	
6.16/2.70		Pol(evalEx1start) = V_1 + 1
6.16/2.70	
6.16/2.70		Pol(koat_start) = V_1 + 1
6.16/2.70	
6.16/2.70	orients all transitions weakly and the transition
6.16/2.70	
6.16/2.70		evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70	strictly and produces the following problem:
6.16/2.70	
6.16/2.70	5:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)           evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)           evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)           evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)           evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Repeatedly propagating knowledge in problem 5 produces the following problem:
6.16/2.70	
6.16/2.70	6:	T:
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)           evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)           evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)    evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)           evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)    evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)           evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)           evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	A polynomial rank function with
6.16/2.70	
6.16/2.70		Pol(evalEx1bb5in) = 1
6.16/2.70	
6.16/2.70		Pol(evalEx1bb6in) = 0
6.16/2.70	
6.16/2.70		Pol(evalEx1bb4in) = 2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb1in) = 2
6.16/2.70	
6.16/2.70	and size complexities
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-0) = 0
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-3) = ar_3
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))", 0-3) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))", 0-0) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))", 0-1) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))", 0-2) = ?
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))", 0-3) = ?
6.16/2.70	
6.16/2.70	orients the transitions
6.16/2.70	
6.16/2.70		evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70		evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70		evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70	weakly and the transitions
6.16/2.70	
6.16/2.70		evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70		evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70	strictly and produces the following problem:
6.16/2.70	
6.16/2.70	7:	T:
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1))
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Applied AI with 'oct' on problem 7 to obtain the following invariants:
6.16/2.70	
6.16/2.70	  For symbol evalEx1bb1in: X_2 - X_4 >= 0 /\ X_4 - 2 >= 0 /\ X_3 + X_4 - 3 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 4 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 - 2 >= 0 /\ X_2 - X_3 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 2 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 - 2 >= 0 /\ X_1 >= 0
6.16/2.70	
6.16/2.70	  For symbol evalEx1bb4in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.16/2.70	
6.16/2.70	  For symbol evalEx1bb5in: X_3 - X_4 >= 0 /\ X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ -X_3 + X_4 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_2 - X_3 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 2 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 - 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.16/2.70	
6.16/2.70	  For symbol evalEx1bb6in: X_1 >= 0
6.16/2.70	
6.16/2.70	  For symbol evalEx1bbin: X_2 - 1 >= 0 /\ X_1 + X_2 - 1 >= 0 /\ -X_1 + X_2 - 1 >= 0 /\ X_1 >= 0
6.16/2.70	
6.16/2.70	  For symbol evalEx1returnin: X_1 - X_2 >= 0 /\ X_1 >= 0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	This yielded the following problem:
6.16/2.70	
6.16/2.70	8:	T:
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	A polynomial rank function with
6.16/2.70	
6.16/2.70		Pol(koat_start) = V_1
6.16/2.70	
6.16/2.70		Pol(evalEx1start) = V_1
6.16/2.70	
6.16/2.70		Pol(evalEx1entryin) = V_1
6.16/2.70	
6.16/2.70		Pol(evalEx1bb6in) = V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1bbin) = V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1returnin) = V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb4in) = V_4
6.16/2.70	
6.16/2.70		Pol(evalEx1stop) = V_2
6.16/2.70	
6.16/2.70		Pol(evalEx1bb1in) = V_4
6.16/2.70	
6.16/2.70		Pol(evalEx1bb5in) = V_4
6.16/2.70	
6.16/2.70	orients all transitions weakly and the transitions
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70	strictly and produces the following problem:
6.16/2.70	
6.16/2.70	9:	T:
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)             evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)      evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)             evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0, Cost: 1)          evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0, Cost: 1)          evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: ?, Cost: 1)             evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)    evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	A polynomial rank function with
6.16/2.70	
6.16/2.70		Pol(evalEx1bb4in) = 2*V_2 - 2*V_3 + 1
6.16/2.70	
6.16/2.70		Pol(evalEx1bb1in) = 2*V_2 - 2*V_3
6.16/2.70	
6.16/2.70	and size complexities
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\\ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ e >= 1 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ e >= 1 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ e >= 1 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ e >= 1 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= e + 1 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= e + 1 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= e + 1 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 2 >= 0 /\\ ar_2 + ar_3 - 3 >= 0 /\\ -ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 4 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 - 2 >= 0 /\\ ar_1 - ar_2 - 1 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 3 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 2 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 - 2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= e + 1 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_3 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_3 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_3 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_2 >= ar_3 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_2 + 1 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_2 + 1 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_2 + 1 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 2 >= 0 /\\ -ar_2 + ar_3 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 1 >= 0 /\\ -ar_0 + ar_3 - 1 >= 0 /\\ ar_1 - ar_2 >= 0 /\\ ar_2 - 1 >= 0 /\\ ar_1 + ar_2 - 2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 - 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 /\\ ar_3 >= ar_2 + 1 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_0 + ar_2
6.16/2.70	
6.16/2.70		S("evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_0 + ar_3
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-2) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 1 >= 0 /\\ -ar_0 + ar_1 - 1 >= 0 /\\ ar_0 >= 0 ]", 0-3) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = ar_0 + ar_2
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-3) = ar_0 + ar_3
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-2) = ar_0 + ar_2
6.16/2.70	
6.16/2.70		S("evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\\ ar_1 >= ar_0 + 1 ]", 0-3) = ar_0 + ar_3
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-0) = 0
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-1) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))", 0-3) = ar_3
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
6.16/2.70	
6.16/2.70		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
6.16/2.70	
6.16/2.70	orients the transitions
6.16/2.70	
6.16/2.70		evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70	weakly and the transitions
6.16/2.70	
6.16/2.70		evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70		evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70	strictly and produces the following problem:
6.16/2.70	
6.16/2.70	10:	T:
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 0)                         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)                         evalEx1start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1entryin(ar_0, ar_1, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: 1, Cost: 1)                         evalEx1entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(0, ar_0, ar_2, ar_3))
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)                  evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bbin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_1 >= ar_0 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)                         evalEx1bb6in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 0 /\ ar_0 >= ar_1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0 + 1, Cost: 1)                  evalEx1bbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_0 + 1, ar_1)) [ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2, Cost: 1)                         evalEx1returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1stop(ar_0, ar_1, ar_2, ar_3)) [ ar_0 - ar_1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 12*ar_0^2 + 7*ar_0 + 1, Cost: 1)    evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_2 + 1 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)                evalEx1bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb5in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_3 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0, Cost: 1)                      evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ 0 >= e + 1 ]
6.16/2.70	
6.16/2.70			(Comp: ar_0, Cost: 1)                      evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 /\ e >= 1 ]
6.16/2.70	
6.16/2.70			(Comp: 12*ar_0^2 + 7*ar_0 + 1, Cost: 1)    evalEx1bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb4in(ar_0, ar_1, ar_2 + 1, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 2 >= 0 /\ ar_2 + ar_3 - 3 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 4 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 - 2 >= 0 /\ ar_1 - ar_2 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 3 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 2 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 - 2 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70			(Comp: 2*ar_0 + 2, Cost: 1)                evalEx1bb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx1bb6in(ar_0 + 1, ar_3, ar_2, ar_3)) [ ar_2 - ar_3 >= 0 /\ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ -ar_2 + ar_3 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_1 - ar_2 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 - 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 1 >= 0 /\ -ar_0 + ar_1 - 1 >= 0 /\ ar_0 >= 0 ]
6.16/2.70	
6.16/2.70		start location:	koat_start
6.16/2.70	
6.16/2.70		leaf cost:	0
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Complexity upper bound 22*ar_0 + 24*ar_0^2 + 14
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Time: 0.519 sec (SMT: 0.409 sec)
6.16/2.70	
6.16/2.70	
6.16/2.70	----------------------------------------
6.16/2.70	
6.16/2.70	(2)
6.16/2.70	BOUNDS(1, n^2)
6.16/2.70	
6.16/2.70	----------------------------------------
6.16/2.70	
6.16/2.70	(3) Loat Proof (FINISHED)
6.16/2.70	
6.16/2.70	
6.16/2.70	### Pre-processing the ITS problem ###
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Initial linear ITS problem
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	      0: evalEx1start -> evalEx1entryin : [], cost: 1
6.16/2.70	
6.16/2.70	      1: evalEx1entryin -> evalEx1bb6in : A'=0, B'=A, [], cost: 1
6.16/2.70	
6.16/2.70	      2: evalEx1bb6in -> evalEx1bbin : [ B>=1+A ], cost: 1
6.16/2.70	
6.16/2.70	      3: evalEx1bb6in -> evalEx1returnin : [ A>=B ], cost: 1
6.16/2.70	
6.16/2.70	      4: evalEx1bbin -> evalEx1bb4in : C'=1+A, D'=B, [], cost: 1
6.16/2.70	
6.16/2.70	      5: evalEx1bb4in -> evalEx1bb1in : [ D>=1+C ], cost: 1
6.16/2.70	
6.16/2.70	      6: evalEx1bb4in -> evalEx1bb5in : [ C>=D ], cost: 1
6.16/2.70	
6.16/2.70	      7: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ 0>=1+free ], cost: 1
6.16/2.70	
6.16/2.70	      8: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ 0>=1+free_1 && free_1>=1 ], cost: 1
6.16/2.70	
6.16/2.70	      9: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ free_2>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     10: evalEx1bb1in -> evalEx1bb4in : [ 0>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     11: evalEx1bb1in -> evalEx1bb4in : C'=1+C, D'=-1+D, [ 0>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     12: evalEx1bb1in -> evalEx1bb4in : C'=1+C, [], cost: 1
6.16/2.70	
6.16/2.70	     13: evalEx1bb5in -> evalEx1bb6in : A'=1+A, B'=D, [], cost: 1
6.16/2.70	
6.16/2.70	     14: evalEx1returnin -> evalEx1stop : [], cost: 1
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Removed unreachable and leaf rules:
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	      0: evalEx1start -> evalEx1entryin : [], cost: 1
6.16/2.70	
6.16/2.70	      1: evalEx1entryin -> evalEx1bb6in : A'=0, B'=A, [], cost: 1
6.16/2.70	
6.16/2.70	      2: evalEx1bb6in -> evalEx1bbin : [ B>=1+A ], cost: 1
6.16/2.70	
6.16/2.70	      4: evalEx1bbin -> evalEx1bb4in : C'=1+A, D'=B, [], cost: 1
6.16/2.70	
6.16/2.70	      5: evalEx1bb4in -> evalEx1bb1in : [ D>=1+C ], cost: 1
6.16/2.70	
6.16/2.70	      6: evalEx1bb4in -> evalEx1bb5in : [ C>=D ], cost: 1
6.16/2.70	
6.16/2.70	      7: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ 0>=1+free ], cost: 1
6.16/2.70	
6.16/2.70	      8: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ 0>=1+free_1 && free_1>=1 ], cost: 1
6.16/2.70	
6.16/2.70	      9: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ free_2>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     10: evalEx1bb1in -> evalEx1bb4in : [ 0>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     11: evalEx1bb1in -> evalEx1bb4in : C'=1+C, D'=-1+D, [ 0>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     12: evalEx1bb1in -> evalEx1bb4in : C'=1+C, [], cost: 1
6.16/2.70	
6.16/2.70	     13: evalEx1bb5in -> evalEx1bb6in : A'=1+A, B'=D, [], cost: 1
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Removed rules with unsatisfiable guard:
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	      0: evalEx1start -> evalEx1entryin : [], cost: 1
6.16/2.70	
6.16/2.70	      1: evalEx1entryin -> evalEx1bb6in : A'=0, B'=A, [], cost: 1
6.16/2.70	
6.16/2.70	      2: evalEx1bb6in -> evalEx1bbin : [ B>=1+A ], cost: 1
6.16/2.70	
6.16/2.70	      4: evalEx1bbin -> evalEx1bb4in : C'=1+A, D'=B, [], cost: 1
6.16/2.70	
6.16/2.70	      5: evalEx1bb4in -> evalEx1bb1in : [ D>=1+C ], cost: 1
6.16/2.70	
6.16/2.70	      6: evalEx1bb4in -> evalEx1bb5in : [ C>=D ], cost: 1
6.16/2.70	
6.16/2.70	      7: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ 0>=1+free ], cost: 1
6.16/2.70	
6.16/2.70	      9: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [ free_2>=1 ], cost: 1
6.16/2.70	
6.16/2.70	     12: evalEx1bb1in -> evalEx1bb4in : C'=1+C, [], cost: 1
6.16/2.70	
6.16/2.70	     13: evalEx1bb5in -> evalEx1bb6in : A'=1+A, B'=D, [], cost: 1
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Simplified all rules, resulting in:
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	      0: evalEx1start -> evalEx1entryin : [], cost: 1
6.16/2.70	
6.16/2.70	      1: evalEx1entryin -> evalEx1bb6in : A'=0, B'=A, [], cost: 1
6.16/2.70	
6.16/2.70	      2: evalEx1bb6in -> evalEx1bbin : [ B>=1+A ], cost: 1
6.16/2.70	
6.16/2.70	      4: evalEx1bbin -> evalEx1bb4in : C'=1+A, D'=B, [], cost: 1
6.16/2.70	
6.16/2.70	      5: evalEx1bb4in -> evalEx1bb1in : [ D>=1+C ], cost: 1
6.16/2.70	
6.16/2.70	      6: evalEx1bb4in -> evalEx1bb5in : [ C>=D ], cost: 1
6.16/2.70	
6.16/2.70	      9: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [], cost: 1
6.16/2.70	
6.16/2.70	     12: evalEx1bb1in -> evalEx1bb4in : C'=1+C, [], cost: 1
6.16/2.70	
6.16/2.70	     13: evalEx1bb5in -> evalEx1bb6in : A'=1+A, B'=D, [], cost: 1
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	### Simplification by acceleration and chaining ###
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Eliminated locations (on linear paths):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     16: evalEx1bb6in -> evalEx1bb4in : C'=1+A, D'=B, [ B>=1+A ], cost: 2
6.16/2.70	
6.16/2.70	      5: evalEx1bb4in -> evalEx1bb1in : [ D>=1+C ], cost: 1
6.16/2.70	
6.16/2.70	     17: evalEx1bb4in -> evalEx1bb6in : A'=1+A, B'=D, [ C>=D ], cost: 2
6.16/2.70	
6.16/2.70	      9: evalEx1bb1in -> evalEx1bb4in : D'=-1+D, [], cost: 1
6.16/2.70	
6.16/2.70	     12: evalEx1bb1in -> evalEx1bb4in : C'=1+C, [], cost: 1
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Eliminated locations (on tree-shaped paths):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     16: evalEx1bb6in -> evalEx1bb4in : C'=1+A, D'=B, [ B>=1+A ], cost: 2
6.16/2.70	
6.16/2.70	     17: evalEx1bb4in -> evalEx1bb6in : A'=1+A, B'=D, [ C>=D ], cost: 2
6.16/2.70	
6.16/2.70	     18: evalEx1bb4in -> evalEx1bb4in : D'=-1+D, [ D>=1+C ], cost: 2
6.16/2.70	
6.16/2.70	     19: evalEx1bb4in -> evalEx1bb4in : C'=1+C, [ D>=1+C ], cost: 2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Accelerating simple loops of location 4.
6.16/2.70	
6.16/2.70	   Accelerating the following rules:
6.16/2.70	
6.16/2.70	     18: evalEx1bb4in -> evalEx1bb4in : D'=-1+D, [ D>=1+C ], cost: 2
6.16/2.70	
6.16/2.70	     19: evalEx1bb4in -> evalEx1bb4in : C'=1+C, [ D>=1+C ], cost: 2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	   Accelerated rule 18 with metering function -C+D, yielding the new rule 20.
6.16/2.70	
6.16/2.70	   Accelerated rule 19 with metering function -C+D, yielding the new rule 21.
6.16/2.70	
6.16/2.70	   Removing the simple loops: 18 19.
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Accelerated all simple loops using metering functions (where possible):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     16: evalEx1bb6in -> evalEx1bb4in : C'=1+A, D'=B, [ B>=1+A ], cost: 2
6.16/2.70	
6.16/2.70	     17: evalEx1bb4in -> evalEx1bb6in : A'=1+A, B'=D, [ C>=D ], cost: 2
6.16/2.70	
6.16/2.70	     20: evalEx1bb4in -> evalEx1bb4in : D'=C, [ D>=1+C ], cost: -2*C+2*D
6.16/2.70	
6.16/2.70	     21: evalEx1bb4in -> evalEx1bb4in : C'=D, [ D>=1+C ], cost: -2*C+2*D
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Chained accelerated rules (with incoming rules):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     16: evalEx1bb6in -> evalEx1bb4in : C'=1+A, D'=B, [ B>=1+A ], cost: 2
6.16/2.70	
6.16/2.70	     22: evalEx1bb6in -> evalEx1bb4in : C'=1+A, D'=1+A, [ B>=2+A ], cost: -2*A+2*B
6.16/2.70	
6.16/2.70	     23: evalEx1bb6in -> evalEx1bb4in : C'=B, D'=B, [ B>=2+A ], cost: -2*A+2*B
6.16/2.70	
6.16/2.70	     17: evalEx1bb4in -> evalEx1bb6in : A'=1+A, B'=D, [ C>=D ], cost: 2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Eliminated locations (on tree-shaped paths):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     24: evalEx1bb6in -> evalEx1bb6in : A'=1+A, B'=B, C'=1+A, D'=B, [ B>=1+A && 1+A>=B ], cost: 4
6.16/2.70	
6.16/2.70	     25: evalEx1bb6in -> evalEx1bb6in : A'=1+A, B'=1+A, C'=1+A, D'=1+A, [ B>=2+A ], cost: 2-2*A+2*B
6.16/2.70	
6.16/2.70	     26: evalEx1bb6in -> evalEx1bb6in : A'=1+A, B'=B, C'=B, D'=B, [ B>=2+A ], cost: 2-2*A+2*B
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Accelerating simple loops of location 2.
6.16/2.70	
6.16/2.70	   Simplified some of the simple loops (and removed duplicate rules).
6.16/2.70	
6.16/2.70	   Accelerating the following rules:
6.16/2.70	
6.16/2.70	     24: evalEx1bb6in -> evalEx1bb6in : A'=1+A, C'=1+A, D'=B, [ 1+A-B==0 ], cost: 4
6.16/2.70	
6.16/2.70	     25: evalEx1bb6in -> evalEx1bb6in : A'=1+A, B'=1+A, C'=1+A, D'=1+A, [ B>=2+A ], cost: 2-2*A+2*B
6.16/2.70	
6.16/2.70	     26: evalEx1bb6in -> evalEx1bb6in : A'=1+A, C'=B, D'=B, [ B>=2+A ], cost: 2-2*A+2*B
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	   Accelerated rule 24 with metering function -A+B, yielding the new rule 27.
6.16/2.70	
6.16/2.70	   Found no metering function for rule 25.
6.16/2.70	
6.16/2.70	   Accelerated rule 26 with metering function -1-A+B, yielding the new rule 28.
6.16/2.70	
6.16/2.70	   Removing the simple loops: 24 26.
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Accelerated all simple loops using metering functions (where possible):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     25: evalEx1bb6in -> evalEx1bb6in : A'=1+A, B'=1+A, C'=1+A, D'=1+A, [ B>=2+A ], cost: 2-2*A+2*B
6.16/2.70	
6.16/2.70	     27: evalEx1bb6in -> evalEx1bb6in : A'=B, C'=B, D'=B, [ 1+A-B==0 ], cost: -4*A+4*B
6.16/2.70	
6.16/2.70	     28: evalEx1bb6in -> evalEx1bb6in : A'=-1+B, C'=B, D'=B, [ B>=2+A ], cost: -3-(1+A-B)^2-3*A-2*(1+A-B)*B+2*A*(1+A-B)+3*B
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Chained accelerated rules (with incoming rules):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     15: evalEx1start -> evalEx1bb6in : A'=0, B'=A, [], cost: 2
6.16/2.70	
6.16/2.70	     29: evalEx1start -> evalEx1bb6in : A'=1, B'=1, C'=1, D'=1, [ A>=2 ], cost: 4+2*A
6.16/2.70	
6.16/2.70	     30: evalEx1start -> evalEx1bb6in : B'=A, C'=A, D'=A, [ 1-A==0 ], cost: 2+4*A
6.16/2.70	
6.16/2.70	     31: evalEx1start -> evalEx1bb6in : A'=-1+A, B'=A, C'=A, D'=A, [ A>=2 ], cost: -1+2*(-1+A)*A+3*A-(-1+A)^2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Removed unreachable locations (and leaf rules with constant cost):
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     29: evalEx1start -> evalEx1bb6in : A'=1, B'=1, C'=1, D'=1, [ A>=2 ], cost: 4+2*A
6.16/2.70	
6.16/2.70	     30: evalEx1start -> evalEx1bb6in : B'=A, C'=A, D'=A, [ 1-A==0 ], cost: 2+4*A
6.16/2.70	
6.16/2.70	     31: evalEx1start -> evalEx1bb6in : A'=-1+A, B'=A, C'=A, D'=A, [ A>=2 ], cost: -1+2*(-1+A)*A+3*A-(-1+A)^2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	### Computing asymptotic complexity ###
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Fully simplified ITS problem
6.16/2.70	
6.16/2.70	   Start location: evalEx1start
6.16/2.70	
6.16/2.70	     29: evalEx1start -> evalEx1bb6in : A'=1, B'=1, C'=1, D'=1, [ A>=2 ], cost: 4+2*A
6.16/2.70	
6.16/2.70	     30: evalEx1start -> evalEx1bb6in : B'=A, C'=A, D'=A, [ 1-A==0 ], cost: 2+4*A
6.16/2.70	
6.16/2.70	     31: evalEx1start -> evalEx1bb6in : A'=-1+A, B'=A, C'=A, D'=A, [ A>=2 ], cost: -1+2*(-1+A)*A+3*A-(-1+A)^2
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Computing asymptotic complexity for rule 29
6.16/2.70	
6.16/2.70	   Solved the limit problem by the following transformations:
6.16/2.70	
6.16/2.70	      Created initial limit problem:
6.16/2.70	
6.16/2.70	      4+2*A (+), -1+A (+/+!) [not solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	      removing all constraints (solved by SMT)
6.16/2.70	
6.16/2.70	      resulting limit problem: [solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	      applying transformation rule (C) using substitution {A==n}
6.16/2.70	
6.16/2.70	      resulting limit problem:
6.16/2.70	
6.16/2.70	      [solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	   Solution:
6.16/2.70	
6.16/2.70	      A / n
6.16/2.70	
6.16/2.70	   Resulting cost 4+2*n has complexity: Poly(n^1)
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Found new complexity Poly(n^1).
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Computing asymptotic complexity for rule 31
6.16/2.70	
6.16/2.70	   Solved the limit problem by the following transformations:
6.16/2.70	
6.16/2.70	      Created initial limit problem:
6.16/2.70	
6.16/2.70	      -1+A (+/+!), -2+3*A+A^2 (+) [not solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	      removing all constraints (solved by SMT)
6.16/2.70	
6.16/2.70	      resulting limit problem: [solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	      applying transformation rule (C) using substitution {A==n}
6.16/2.70	
6.16/2.70	      resulting limit problem:
6.16/2.70	
6.16/2.70	      [solved]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	   Solution:
6.16/2.70	
6.16/2.70	      A / n
6.16/2.70	
6.16/2.70	   Resulting cost -2+3*n+n^2 has complexity: Poly(n^2)
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Found new complexity Poly(n^2).
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	Obtained the following overall complexity (w.r.t. the length of the input n):
6.16/2.70	
6.16/2.70	   Complexity:  Poly(n^2)
6.16/2.70	
6.16/2.70	   Cpx degree:  2
6.16/2.70	
6.16/2.70	   Solved cost: -2+3*n+n^2
6.16/2.70	
6.16/2.70	   Rule cost:   -1+2*(-1+A)*A+3*A-(-1+A)^2
6.16/2.70	
6.16/2.70	   Rule guard:  [ A>=2 ]
6.16/2.70	
6.16/2.70	
6.16/2.70	
6.16/2.70	WORST_CASE(Omega(n^2),?)
6.16/2.70	
6.16/2.70	
6.16/2.70	----------------------------------------
6.16/2.70	
6.16/2.70	(4)
6.16/2.70	BOUNDS(n^2, INF)
6.32/2.73	EOF