5.66/2.55	WORST_CASE(Omega(n^1), O(n^2))
5.66/2.56	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.66/2.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.66/2.56	
5.66/2.56	
5.66/2.56	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^2).
5.66/2.56	
5.66/2.56	(0) CpxIntTrs
5.66/2.56	(1) Koat Proof [FINISHED, 932 ms]
5.66/2.56	(2) BOUNDS(1, n^2)
5.66/2.56	(3) Loat Proof [FINISHED, 537 ms]
5.66/2.56	(4) BOUNDS(n^1, INF)
5.66/2.56	
5.66/2.56	
5.66/2.56	----------------------------------------
5.66/2.56	
5.66/2.56	(0)
5.66/2.56	Obligation:
5.66/2.56	Complexity Int TRS consisting of the following rules:
5.66/2.56	evalrsdstart(A, B, C) -> Com_1(evalrsdentryin(A, B, C)) :|: TRUE
5.66/2.56	evalrsdentryin(A, B, C) -> Com_1(evalrsdbbin(A, B, C)) :|: A >= 0
5.66/2.56	evalrsdentryin(A, B, C) -> Com_1(evalrsdreturnin(A, B, C)) :|: 0 >= A + 1
5.66/2.56	evalrsdbbin(A, B, C) -> Com_1(evalrsdbb4in(A, 2 * A, 2 * A)) :|: TRUE
5.66/2.56	evalrsdbb4in(A, B, C) -> Com_1(evalrsdbb1in(A, B, C)) :|: C >= A
5.66/2.56	evalrsdbb4in(A, B, C) -> Com_1(evalrsdreturnin(A, B, C)) :|: A >= C + 1
5.66/2.56	evalrsdbb1in(A, B, C) -> Com_1(evalrsdbb2in(A, B, C)) :|: 0 >= D + 1
5.66/2.56	evalrsdbb1in(A, B, C) -> Com_1(evalrsdbb2in(A, B, C)) :|: D >= 1
5.66/2.56	evalrsdbb1in(A, B, C) -> Com_1(evalrsdbb3in(A, B, C)) :|: TRUE
5.66/2.56	evalrsdbb2in(A, B, C) -> Com_1(evalrsdbb4in(A, B, C - 1)) :|: TRUE
5.66/2.56	evalrsdbb3in(A, B, C) -> Com_1(evalrsdbb4in(A, B - 1, B - 1)) :|: TRUE
5.66/2.56	evalrsdreturnin(A, B, C) -> Com_1(evalrsdstop(A, B, C)) :|: TRUE
5.66/2.56	
5.66/2.56	The start-symbols are:[evalrsdstart_3]
5.66/2.56	
5.66/2.56	
5.66/2.56	----------------------------------------
5.66/2.56	
5.66/2.56	(1) Koat Proof (FINISHED)
5.66/2.56	YES(?, 36*ar_0 + 40*ar_0^2 + 19)
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Initial complexity problem:
5.66/2.56	
5.66/2.56	1:	T:
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.66/2.56	
5.66/2.56	2:	T:
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	A polynomial rank function with
5.66/2.56	
5.66/2.56		Pol(evalrsdstart) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdentryin) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdbbin) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdreturnin) = 1
5.66/2.56	
5.66/2.56		Pol(evalrsdbb4in) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdbb1in) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdbb2in) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdbb3in) = 2
5.66/2.56	
5.66/2.56		Pol(evalrsdstop) = 0
5.66/2.56	
5.66/2.56		Pol(koat_start) = 2
5.66/2.56	
5.66/2.56	orients all transitions weakly and the transitions
5.66/2.56	
5.66/2.56		evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56		evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56	strictly and produces the following problem:
5.66/2.56	
5.66/2.56	3:	T:
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1))
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Applied AI with 'oct' on problem 3 to obtain the following invariants:
5.66/2.56	
5.66/2.56	  For symbol evalrsdbb1in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0
5.66/2.56	
5.66/2.56	  For symbol evalrsdbb2in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0
5.66/2.56	
5.66/2.56	  For symbol evalrsdbb3in: X_3 >= 0 /\ X_1 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ X_1 >= 0
5.66/2.56	
5.66/2.56	  For symbol evalrsdbb4in: X_1 >= 0
5.66/2.56	
5.66/2.56	  For symbol evalrsdbbin: X_1 >= 0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	This yielded the following problem:
5.66/2.56	
5.66/2.56	4:	T:
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	By chaining the transition koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdstart(ar_0, ar_1, ar_2)) [ 0 <= 0 ] with all transitions in problem 4, the following new transition is obtained:
5.66/2.56	
5.66/2.56		koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	5:	T:
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Testing for reachability in the complexity graph removes the following transition from problem 5:
5.66/2.56	
5.66/2.56		evalrsdstart(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	6:	T:
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	By chaining the transition evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ] with all transitions in problem 6, the following new transition is obtained:
5.66/2.56	
5.66/2.56		evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	7:	T:
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	By chaining the transition evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ] with all transitions in problem 7, the following new transition is obtained:
5.66/2.56	
5.66/2.56		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	8:	T:
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	By chaining the transition evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb2in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ] with all transitions in problem 8, the following new transition is obtained:
5.66/2.56	
5.66/2.56		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	9:	T:
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Testing for reachability in the complexity graph removes the following transition from problem 9:
5.66/2.56	
5.66/2.56		evalrsdbb2in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	10:	T:
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	By chaining the transition evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb3in(ar_0, ar_1, ar_2)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ] with all transitions in problem 10, the following new transition is obtained:
5.66/2.56	
5.66/2.56		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	11:	T:
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.56	
5.66/2.56		start location:	koat_start
5.66/2.56	
5.66/2.56		leaf cost:	0
5.66/2.56	
5.66/2.56	
5.66/2.56	
5.66/2.56	Testing for reachability in the complexity graph removes the following transition from problem 11:
5.66/2.56	
5.66/2.56		evalrsdbb3in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.56	
5.66/2.56	We thus obtain the following problem:
5.66/2.56	
5.66/2.56	12:	T:
5.66/2.56	
5.66/2.56			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.56	
5.66/2.56			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	By chaining the transition evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 ] with all transitions in problem 12, the following new transition is obtained:
5.66/2.57	
5.66/2.57		evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	13:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	By chaining the transition evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbbin(ar_0, ar_1, ar_2)) [ ar_0 >= 0 ] with all transitions in problem 13, the following new transition is obtained:
5.66/2.57	
5.66/2.57		evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	14:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Testing for reachability in the complexity graph removes the following transition from problem 14:
5.66/2.57	
5.66/2.57		evalrsdbbin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	15:	T:
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	By chaining the transition evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdreturnin(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ] with all transitions in problem 15, the following new transition is obtained:
5.66/2.57	
5.66/2.57		evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	16:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 1)    evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Testing for reachability in the complexity graph removes the following transition from problem 16:
5.66/2.57	
5.66/2.57		evalrsdreturnin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2))
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	17:	T:
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	By chaining the transition evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 ] with all transitions in problem 17, the following new transitions are obtained:
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57	We thus obtain the following problem:
5.66/2.57	
5.66/2.57	18:	T:
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 4)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 3)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	A polynomial rank function with
5.66/2.57	
5.66/2.57		Pol(evalrsdbb1in) = 1
5.66/2.57	
5.66/2.57		Pol(evalrsdstop) = 0
5.66/2.57	
5.66/2.57		Pol(evalrsdbb4in) = 1
5.66/2.57	
5.66/2.57		Pol(evalrsdentryin) = 1
5.66/2.57	
5.66/2.57		Pol(koat_start) = 1
5.66/2.57	
5.66/2.57	orients all transitions weakly and the transition
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57	strictly and produces the following problem:
5.66/2.57	
5.66/2.57	19:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 4)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 3)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)    evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)    koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	A polynomial rank function with
5.66/2.57	
5.66/2.57		Pol(evalrsdbb4in) = V_2
5.66/2.57	
5.66/2.57		Pol(evalrsdbb1in) = V_2
5.66/2.57	
5.66/2.57	and size complexities
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-2) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-2) = 2*ar_0 + 16
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-2) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = 2*ar_0 + 2
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = 2*ar_0 + 2
5.66/2.57	
5.66/2.57	orients the transitions
5.66/2.57	
5.66/2.57		evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57	weakly and the transition
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57	strictly and produces the following problem:
5.66/2.57	
5.66/2.57	20:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 4)         evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: 2*ar_0, Cost: 3)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)         evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 1)         evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)         evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: ?, Cost: 2)         evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)         evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)         evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)         koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	A polynomial rank function with
5.66/2.57	
5.66/2.57		Pol(evalrsdbb4in) = 2*V_3 + 2
5.66/2.57	
5.66/2.57		Pol(evalrsdbb1in) = 2*V_3 + 1
5.66/2.57	
5.66/2.57	and size complexities
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\\ 2*ar_0 >= ar_0 ]", 0-2) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-1) = ar_1
5.66/2.57	
5.66/2.57		S("evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]", 0-2) = ar_2
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ 0 >= d + 1 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ d >= 1 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_2 >= ar_0 ]", 0-2) = 2*ar_0 + 8
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\\ ar_0 >= ar_2 + 1 ]", 0-2) = 2*ar_0 + 16
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-1) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_1 - 1 >= ar_0 ]", 0-2) = 2*ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-0) = ar_0
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-1) = 2*ar_0 + 2
5.66/2.57	
5.66/2.57		S("evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\\ ar_0 + ar_2 >= 0 /\\ -ar_0 + ar_2 >= 0 /\\ ar_0 >= 0 /\\ ar_0 >= ar_1 ]", 0-2) = 2*ar_0 + 2
5.66/2.57	
5.66/2.57	orients the transitions
5.66/2.57	
5.66/2.57		evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57	weakly and the transitions
5.66/2.57	
5.66/2.57		evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57		evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57	strictly and produces the following problem:
5.66/2.57	
5.66/2.57	21:	T:
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 4)                        evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_1 ]
5.66/2.57	
5.66/2.57			(Comp: 2*ar_0, Cost: 3)                   evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1 - 1, ar_1 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ ar_1 - 1 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 2, Cost: 2)                        evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_0 >= ar_2 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 8*ar_0^2 + 6*ar_0 + 1, Cost: 1)    evalrsdbb4in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, ar_1, ar_2)) [ ar_0 >= 0 /\ ar_2 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 8*ar_0^2 + 6*ar_0 + 1, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ d >= 1 ]
5.66/2.57	
5.66/2.57			(Comp: 8*ar_0^2 + 6*ar_0 + 1, Cost: 2)    evalrsdbb1in(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb4in(ar_0, ar_1, ar_2 - 1)) [ ar_2 >= 0 /\ ar_0 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ ar_0 >= 0 /\ 0 >= d + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 2)                        evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdstop(ar_0, ar_1, ar_2)) [ 0 >= ar_0 + 1 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 3)                        evalrsdentryin(ar_0, ar_1, ar_2) -> Com_1(evalrsdbb1in(ar_0, 2*ar_0, 2*ar_0)) [ ar_0 >= 0 /\ 2*ar_0 >= ar_0 ]
5.66/2.57	
5.66/2.57			(Comp: 1, Cost: 1)                        koat_start(ar_0, ar_1, ar_2) -> Com_1(evalrsdentryin(ar_0, ar_1, ar_2)) [ 0 <= 0 ]
5.66/2.57	
5.66/2.57		start location:	koat_start
5.66/2.57	
5.66/2.57		leaf cost:	0
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Complexity upper bound 36*ar_0 + 40*ar_0^2 + 19
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Time: 0.946 sec (SMT: 0.806 sec)
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(2)
5.66/2.57	BOUNDS(1, n^2)
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(3) Loat Proof (FINISHED)
5.66/2.57	
5.66/2.57	
5.66/2.57	### Pre-processing the ITS problem ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Initial linear ITS problem
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	      0: evalrsdstart -> evalrsdentryin : [], cost: 1
5.66/2.57	
5.66/2.57	      1: evalrsdentryin -> evalrsdbbin : [ A>=0 ], cost: 1
5.66/2.57	
5.66/2.57	      2: evalrsdentryin -> evalrsdreturnin : [ 0>=1+A ], cost: 1
5.66/2.57	
5.66/2.57	      3: evalrsdbbin -> evalrsdbb4in : B'=2*A, C'=2*A, [], cost: 1
5.66/2.57	
5.66/2.57	      4: evalrsdbb4in -> evalrsdbb1in : [ C>=A ], cost: 1
5.66/2.57	
5.66/2.57	      5: evalrsdbb4in -> evalrsdreturnin : [ A>=1+C ], cost: 1
5.66/2.57	
5.66/2.57	      6: evalrsdbb1in -> evalrsdbb2in : [ 0>=1+free ], cost: 1
5.66/2.57	
5.66/2.57	      7: evalrsdbb1in -> evalrsdbb2in : [ free_1>=1 ], cost: 1
5.66/2.57	
5.66/2.57	      8: evalrsdbb1in -> evalrsdbb3in : [], cost: 1
5.66/2.57	
5.66/2.57	      9: evalrsdbb2in -> evalrsdbb4in : C'=-1+C, [], cost: 1
5.66/2.57	
5.66/2.57	     10: evalrsdbb3in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [], cost: 1
5.66/2.57	
5.66/2.57	     11: evalrsdreturnin -> evalrsdstop : [], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Removed unreachable and leaf rules:
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	      0: evalrsdstart -> evalrsdentryin : [], cost: 1
5.66/2.57	
5.66/2.57	      1: evalrsdentryin -> evalrsdbbin : [ A>=0 ], cost: 1
5.66/2.57	
5.66/2.57	      3: evalrsdbbin -> evalrsdbb4in : B'=2*A, C'=2*A, [], cost: 1
5.66/2.57	
5.66/2.57	      4: evalrsdbb4in -> evalrsdbb1in : [ C>=A ], cost: 1
5.66/2.57	
5.66/2.57	      6: evalrsdbb1in -> evalrsdbb2in : [ 0>=1+free ], cost: 1
5.66/2.57	
5.66/2.57	      7: evalrsdbb1in -> evalrsdbb2in : [ free_1>=1 ], cost: 1
5.66/2.57	
5.66/2.57	      8: evalrsdbb1in -> evalrsdbb3in : [], cost: 1
5.66/2.57	
5.66/2.57	      9: evalrsdbb2in -> evalrsdbb4in : C'=-1+C, [], cost: 1
5.66/2.57	
5.66/2.57	     10: evalrsdbb3in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Simplified all rules, resulting in:
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	      0: evalrsdstart -> evalrsdentryin : [], cost: 1
5.66/2.57	
5.66/2.57	      1: evalrsdentryin -> evalrsdbbin : [ A>=0 ], cost: 1
5.66/2.57	
5.66/2.57	      3: evalrsdbbin -> evalrsdbb4in : B'=2*A, C'=2*A, [], cost: 1
5.66/2.57	
5.66/2.57	      4: evalrsdbb4in -> evalrsdbb1in : [ C>=A ], cost: 1
5.66/2.57	
5.66/2.57	      7: evalrsdbb1in -> evalrsdbb2in : [], cost: 1
5.66/2.57	
5.66/2.57	      8: evalrsdbb1in -> evalrsdbb3in : [], cost: 1
5.66/2.57	
5.66/2.57	      9: evalrsdbb2in -> evalrsdbb4in : C'=-1+C, [], cost: 1
5.66/2.57	
5.66/2.57	     10: evalrsdbb3in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [], cost: 1
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	### Simplification by acceleration and chaining ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Eliminated locations (on linear paths):
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     13: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=2*A, [ A>=0 ], cost: 3
5.66/2.57	
5.66/2.57	      4: evalrsdbb4in -> evalrsdbb1in : [ C>=A ], cost: 1
5.66/2.57	
5.66/2.57	     14: evalrsdbb1in -> evalrsdbb4in : C'=-1+C, [], cost: 2
5.66/2.57	
5.66/2.57	     15: evalrsdbb1in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [], cost: 2
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Eliminated locations (on tree-shaped paths):
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     13: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=2*A, [ A>=0 ], cost: 3
5.66/2.57	
5.66/2.57	     16: evalrsdbb4in -> evalrsdbb4in : C'=-1+C, [ C>=A ], cost: 3
5.66/2.57	
5.66/2.57	     17: evalrsdbb4in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [ C>=A ], cost: 3
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerating simple loops of location 3.
5.66/2.57	
5.66/2.57	   Accelerating the following rules:
5.66/2.57	
5.66/2.57	     16: evalrsdbb4in -> evalrsdbb4in : C'=-1+C, [ C>=A ], cost: 3
5.66/2.57	
5.66/2.57	     17: evalrsdbb4in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [ C>=A ], cost: 3
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Accelerated rule 16 with metering function 1+C-A, yielding the new rule 18.
5.66/2.57	
5.66/2.57	   Found no metering function for rule 17.
5.66/2.57	
5.66/2.57	   Removing the simple loops: 16.
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Accelerated all simple loops using metering functions (where possible):
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     13: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=2*A, [ A>=0 ], cost: 3
5.66/2.57	
5.66/2.57	     17: evalrsdbb4in -> evalrsdbb4in : B'=-1+B, C'=-1+B, [ C>=A ], cost: 3
5.66/2.57	
5.66/2.57	     18: evalrsdbb4in -> evalrsdbb4in : C'=-1+A, [ C>=A ], cost: 3+3*C-3*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Chained accelerated rules (with incoming rules):
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     13: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=2*A, [ A>=0 ], cost: 3
5.66/2.57	
5.66/2.57	     19: evalrsdstart -> evalrsdbb4in : B'=-1+2*A, C'=-1+2*A, [ A>=0 ], cost: 6
5.66/2.57	
5.66/2.57	     20: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=-1+A, [ A>=0 ], cost: 6+3*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Removed unreachable locations (and leaf rules with constant cost):
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     20: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=-1+A, [ A>=0 ], cost: 6+3*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	### Computing asymptotic complexity ###
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Fully simplified ITS problem
5.66/2.57	
5.66/2.57	   Start location: evalrsdstart
5.66/2.57	
5.66/2.57	     20: evalrsdstart -> evalrsdbb4in : B'=2*A, C'=-1+A, [ A>=0 ], cost: 6+3*A
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Computing asymptotic complexity for rule 20
5.66/2.57	
5.66/2.57	   Solved the limit problem by the following transformations:
5.66/2.57	
5.66/2.57	      Created initial limit problem:
5.66/2.57	
5.66/2.57	      6+3*A (+), 1+A (+/+!) [not solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      removing all constraints (solved by SMT)
5.66/2.57	
5.66/2.57	      resulting limit problem: [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	      applying transformation rule (C) using substitution {A==n}
5.66/2.57	
5.66/2.57	      resulting limit problem:
5.66/2.57	
5.66/2.57	      [solved]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	   Solution:
5.66/2.57	
5.66/2.57	      A / n
5.66/2.57	
5.66/2.57	   Resulting cost 6+3*n has complexity: Poly(n^1)
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Found new complexity Poly(n^1).
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	Obtained the following overall complexity (w.r.t. the length of the input n):
5.66/2.57	
5.66/2.57	   Complexity:  Poly(n^1)
5.66/2.57	
5.66/2.57	   Cpx degree:  1
5.66/2.57	
5.66/2.57	   Solved cost: 6+3*n
5.66/2.57	
5.66/2.57	   Rule cost:   6+3*A
5.66/2.57	
5.66/2.57	   Rule guard:  [ A>=0 ]
5.66/2.57	
5.66/2.57	
5.66/2.57	
5.66/2.57	WORST_CASE(Omega(n^1),?)
5.66/2.57	
5.66/2.57	
5.66/2.57	----------------------------------------
5.66/2.57	
5.66/2.57	(4)
5.66/2.57	BOUNDS(n^1, INF)
5.79/2.60	EOF