4.61/2.24	WORST_CASE(Omega(n^1), O(n^1))
4.61/2.25	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.61/2.25	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.61/2.25	
4.61/2.25	
4.61/2.25	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
4.61/2.25	
4.61/2.25	(0) CpxIntTrs
4.61/2.25	(1) Koat Proof [FINISHED, 216 ms]
4.61/2.25	(2) BOUNDS(1, n^1)
4.61/2.25	(3) Loat Proof [FINISHED, 533 ms]
4.61/2.25	(4) BOUNDS(n^1, INF)
4.61/2.25	
4.61/2.25	
4.61/2.25	----------------------------------------
4.61/2.25	
4.61/2.25	(0)
4.61/2.25	Obligation:
4.61/2.25	Complexity Int TRS consisting of the following rules:
4.61/2.25	evalSimpleMultiplestart(A, B, C, D) -> Com_1(evalSimpleMultipleentryin(A, B, C, D)) :|: TRUE
4.61/2.25	evalSimpleMultipleentryin(A, B, C, D) -> Com_1(evalSimpleMultiplebb3in(0, 0, C, D)) :|: TRUE
4.61/2.25	evalSimpleMultiplebb3in(A, B, C, D) -> Com_1(evalSimpleMultiplebbin(A, B, C, D)) :|: C >= B + 1
4.61/2.25	evalSimpleMultiplebb3in(A, B, C, D) -> Com_1(evalSimpleMultiplereturnin(A, B, C, D)) :|: B >= C
4.61/2.25	evalSimpleMultiplebbin(A, B, C, D) -> Com_1(evalSimpleMultiplebb1in(A, B, C, D)) :|: D >= A + 1
4.61/2.25	evalSimpleMultiplebbin(A, B, C, D) -> Com_1(evalSimpleMultiplebb2in(A, B, C, D)) :|: A >= D
4.61/2.26	evalSimpleMultiplebb1in(A, B, C, D) -> Com_1(evalSimpleMultiplebb3in(A + 1, B, C, D)) :|: TRUE
4.61/2.26	evalSimpleMultiplebb2in(A, B, C, D) -> Com_1(evalSimpleMultiplebb3in(A, B + 1, C, D)) :|: TRUE
4.61/2.26	evalSimpleMultiplereturnin(A, B, C, D) -> Com_1(evalSimpleMultiplestop(A, B, C, D)) :|: TRUE
4.61/2.26	
4.61/2.26	The start-symbols are:[evalSimpleMultiplestart_4]
4.61/2.26	
4.61/2.26	
4.61/2.26	----------------------------------------
4.61/2.26	
4.61/2.26	(1) Koat Proof (FINISHED)
4.61/2.26	YES(?, 6*ar_2 + 3*ar_3 + 10)
4.61/2.26	
4.61/2.26	
4.61/2.26	
4.61/2.26	Initial complexity problem:
4.61/2.26	
4.61/2.26	1:	T:
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3))
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3))
4.61/2.26	
4.61/2.26			(Comp: ?, Cost: 1)    evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.26	
4.61/2.26			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.26	
4.61/2.26		start location:	koat_start
4.61/2.26	
4.61/2.26		leaf cost:	0
4.61/2.26	
4.61/2.26	
4.61/2.26	
4.61/2.26	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.61/2.26	
4.61/2.26	2:	T:
4.61/2.26	
4.61/2.26			(Comp: 1, Cost: 1)    evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)    evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	A polynomial rank function with
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestart) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultipleentryin) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb3in) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebbin) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplereturnin) = 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb1in) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb2in) = 2
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestop) = 0
4.61/2.27	
4.61/2.27		Pol(koat_start) = 2
4.61/2.27	
4.61/2.27	orients all transitions weakly and the transitions
4.61/2.27	
4.61/2.27		evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27		evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27	strictly and produces the following problem:
4.61/2.27	
4.61/2.27	3:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)    evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)    evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)    evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)    evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	A polynomial rank function with
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestart) = V_4 + 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultipleentryin) = V_4 + 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb3in) = -V_1 + V_4 + 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebbin) = -V_1 + V_4 + 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplereturnin) = -V_1 + V_4
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb1in) = -V_1 + V_4
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb2in) = -V_1 + V_4 + 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestop) = -V_1 + V_4
4.61/2.27	
4.61/2.27		Pol(koat_start) = V_4 + 1
4.61/2.27	
4.61/2.27	orients all transitions weakly and the transition
4.61/2.27	
4.61/2.27		evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27	strictly and produces the following problem:
4.61/2.27	
4.61/2.27	4:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.61/2.27	
4.61/2.27	5:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Applied AI with 'oct' on problem 5 to obtain the following invariants:
4.61/2.27	
4.61/2.27	  For symbol evalSimpleMultiplebb1in: X_4 - 1 >= 0 /\ X_3 + X_4 - 2 >= 0 /\ X_2 + X_4 - 1 >= 0 /\ X_1 + X_4 - 1 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.61/2.27	
4.61/2.27	  For symbol evalSimpleMultiplebb2in: X_1 - X_4 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.61/2.27	
4.61/2.27	  For symbol evalSimpleMultiplebb3in: X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.61/2.27	
4.61/2.27	  For symbol evalSimpleMultiplebbin: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ -X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.61/2.27	
4.61/2.27	  For symbol evalSimpleMultiplereturnin: X_2 - X_3 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ X_1 >= 0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	This yielded the following problem:
4.61/2.27	
4.61/2.27	6:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_0 - ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	A polynomial rank function with
4.61/2.27	
4.61/2.27		Pol(koat_start) = 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestart) = 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplereturnin) = -2*V_2 + 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplestop) = -2*V_2 + 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb2in) = -2*V_2 + 2*V_3 - 1
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb3in) = -2*V_2 + 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebb1in) = -2*V_2 + 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultiplebbin) = -2*V_2 + 2*V_3
4.61/2.27	
4.61/2.27		Pol(evalSimpleMultipleentryin) = 2*V_3
4.61/2.27	
4.61/2.27	orients all transitions weakly and the transitions
4.61/2.27	
4.61/2.27		evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27		evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_0 - ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27	strictly and produces the following problem:
4.61/2.27	
4.61/2.27	7:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)           koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2*ar_2, Cost: 1)      evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_0 - ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2*ar_2, Cost: 1)      evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)    evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ?, Cost: 1)           evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)           evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Repeatedly propagating knowledge in problem 7 produces the following problem:
4.61/2.27	
4.61/2.27	8:	T:
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 0)                    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)                    evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplestop(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_2 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2*ar_2, Cost: 1)               evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0, ar_1 + 1, ar_2, ar_3)) [ ar_0 - ar_3 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)             evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(ar_0 + 1, ar_1, ar_2, ar_3)) [ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 2 >= 0 /\ ar_1 + ar_3 - 1 >= 0 /\ ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 ]
4.61/2.27	
4.61/2.27			(Comp: 2*ar_2, Cost: 1)               evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_0 >= ar_3 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 1, Cost: 1)             evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 - 1 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ -ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_3 >= ar_0 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 2, Cost: 1)                    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplereturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_1 >= ar_2 ]
4.61/2.27	
4.61/2.27			(Comp: ar_3 + 2*ar_2 + 2, Cost: 1)    evalSimpleMultiplebb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= 0 /\ ar_0 + ar_1 >= 0 /\ ar_0 >= 0 /\ ar_2 >= ar_1 + 1 ]
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)                    evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultiplebb3in(0, 0, ar_2, ar_3))
4.61/2.27	
4.61/2.27			(Comp: 1, Cost: 1)                    evalSimpleMultiplestart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalSimpleMultipleentryin(ar_0, ar_1, ar_2, ar_3))
4.61/2.27	
4.61/2.27		start location:	koat_start
4.61/2.27	
4.61/2.27		leaf cost:	0
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Complexity upper bound 6*ar_2 + 3*ar_3 + 10
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Time: 0.254 sec (SMT: 0.223 sec)
4.61/2.27	
4.61/2.27	
4.61/2.27	----------------------------------------
4.61/2.27	
4.61/2.27	(2)
4.61/2.27	BOUNDS(1, n^1)
4.61/2.27	
4.61/2.27	----------------------------------------
4.61/2.27	
4.61/2.27	(3) Loat Proof (FINISHED)
4.61/2.27	
4.61/2.27	
4.61/2.27	### Pre-processing the ITS problem ###
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Initial linear ITS problem
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      0: evalSimpleMultiplestart -> evalSimpleMultipleentryin : [], cost: 1
4.61/2.27	
4.61/2.27	      1: evalSimpleMultipleentryin -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 1
4.61/2.27	
4.61/2.27	      2: evalSimpleMultiplebb3in -> evalSimpleMultiplebbin : [ C>=1+B ], cost: 1
4.61/2.27	
4.61/2.27	      3: evalSimpleMultiplebb3in -> evalSimpleMultiplereturnin : [ B>=C ], cost: 1
4.61/2.27	
4.61/2.27	      4: evalSimpleMultiplebbin -> evalSimpleMultiplebb1in : [ D>=1+A ], cost: 1
4.61/2.27	
4.61/2.27	      5: evalSimpleMultiplebbin -> evalSimpleMultiplebb2in : [ A>=D ], cost: 1
4.61/2.27	
4.61/2.27	      6: evalSimpleMultiplebb1in -> evalSimpleMultiplebb3in : A'=1+A, [], cost: 1
4.61/2.27	
4.61/2.27	      7: evalSimpleMultiplebb2in -> evalSimpleMultiplebb3in : B'=1+B, [], cost: 1
4.61/2.27	
4.61/2.27	      8: evalSimpleMultiplereturnin -> evalSimpleMultiplestop : [], cost: 1
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Removed unreachable and leaf rules:
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      0: evalSimpleMultiplestart -> evalSimpleMultipleentryin : [], cost: 1
4.61/2.27	
4.61/2.27	      1: evalSimpleMultipleentryin -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 1
4.61/2.27	
4.61/2.27	      2: evalSimpleMultiplebb3in -> evalSimpleMultiplebbin : [ C>=1+B ], cost: 1
4.61/2.27	
4.61/2.27	      4: evalSimpleMultiplebbin -> evalSimpleMultiplebb1in : [ D>=1+A ], cost: 1
4.61/2.27	
4.61/2.27	      5: evalSimpleMultiplebbin -> evalSimpleMultiplebb2in : [ A>=D ], cost: 1
4.61/2.27	
4.61/2.27	      6: evalSimpleMultiplebb1in -> evalSimpleMultiplebb3in : A'=1+A, [], cost: 1
4.61/2.27	
4.61/2.27	      7: evalSimpleMultiplebb2in -> evalSimpleMultiplebb3in : B'=1+B, [], cost: 1
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	### Simplification by acceleration and chaining ###
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Eliminated locations (on linear paths):
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      9: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 2
4.61/2.27	
4.61/2.27	      2: evalSimpleMultiplebb3in -> evalSimpleMultiplebbin : [ C>=1+B ], cost: 1
4.61/2.27	
4.61/2.27	     10: evalSimpleMultiplebbin -> evalSimpleMultiplebb3in : A'=1+A, [ D>=1+A ], cost: 2
4.61/2.27	
4.61/2.27	     11: evalSimpleMultiplebbin -> evalSimpleMultiplebb3in : B'=1+B, [ A>=D ], cost: 2
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Eliminated locations (on tree-shaped paths):
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      9: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 2
4.61/2.27	
4.61/2.27	     12: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : A'=1+A, [ C>=1+B && D>=1+A ], cost: 3
4.61/2.27	
4.61/2.27	     13: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : B'=1+B, [ C>=1+B && A>=D ], cost: 3
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Accelerating simple loops of location 2.
4.61/2.27	
4.61/2.27	   Accelerating the following rules:
4.61/2.27	
4.61/2.27	     12: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : A'=1+A, [ C>=1+B && D>=1+A ], cost: 3
4.61/2.27	
4.61/2.27	     13: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : B'=1+B, [ C>=1+B && A>=D ], cost: 3
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	   Accelerated rule 12 with metering function D-A, yielding the new rule 14.
4.61/2.27	
4.61/2.27	   Accelerated rule 13 with metering function C-B, yielding the new rule 15.
4.61/2.27	
4.61/2.27	   Removing the simple loops: 12 13.
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Accelerated all simple loops using metering functions (where possible):
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      9: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 2
4.61/2.27	
4.61/2.27	     14: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : A'=D, [ C>=1+B && D>=1+A ], cost: 3*D-3*A
4.61/2.27	
4.61/2.27	     15: evalSimpleMultiplebb3in -> evalSimpleMultiplebb3in : B'=C, [ C>=1+B && A>=D ], cost: 3*C-3*B
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Chained accelerated rules (with incoming rules):
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	      9: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=0, [], cost: 2
4.61/2.27	
4.61/2.27	     16: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=D, B'=0, [ C>=1 && D>=1 ], cost: 2+3*D
4.61/2.27	
4.61/2.27	     17: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=C, [ C>=1 && 0>=D ], cost: 2+3*C
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Removed unreachable locations (and leaf rules with constant cost):
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	     16: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=D, B'=0, [ C>=1 && D>=1 ], cost: 2+3*D
4.61/2.27	
4.61/2.27	     17: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=C, [ C>=1 && 0>=D ], cost: 2+3*C
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	### Computing asymptotic complexity ###
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Fully simplified ITS problem
4.61/2.27	
4.61/2.27	   Start location: evalSimpleMultiplestart
4.61/2.27	
4.61/2.27	     16: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=D, B'=0, [ C>=1 && D>=1 ], cost: 2+3*D
4.61/2.27	
4.61/2.27	     17: evalSimpleMultiplestart -> evalSimpleMultiplebb3in : A'=0, B'=C, [ C>=1 && 0>=D ], cost: 2+3*C
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Computing asymptotic complexity for rule 16
4.61/2.27	
4.61/2.27	   Solved the limit problem by the following transformations:
4.61/2.27	
4.61/2.27	      Created initial limit problem:
4.61/2.27	
4.61/2.27	      C (+/+!), D (+/+!), 2+3*D (+) [not solved]
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	      removing all constraints (solved by SMT)
4.61/2.27	
4.61/2.27	      resulting limit problem: [solved]
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	      applying transformation rule (C) using substitution {C==1,D==n}
4.61/2.27	
4.61/2.27	      resulting limit problem:
4.61/2.27	
4.61/2.27	      [solved]
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	   Solution:
4.61/2.27	
4.61/2.27	      C / 1
4.61/2.27	
4.61/2.27	      D / n
4.61/2.27	
4.61/2.27	   Resulting cost 2+3*n has complexity: Poly(n^1)
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Found new complexity Poly(n^1).
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	Obtained the following overall complexity (w.r.t. the length of the input n):
4.61/2.27	
4.61/2.27	   Complexity:  Poly(n^1)
4.61/2.27	
4.61/2.27	   Cpx degree:  1
4.61/2.27	
4.61/2.27	   Solved cost: 2+3*n
4.61/2.27	
4.61/2.27	   Rule cost:   2+3*D
4.61/2.27	
4.61/2.27	   Rule guard:  [ C>=1 && D>=1 ]
4.61/2.27	
4.61/2.27	
4.61/2.27	
4.61/2.27	WORST_CASE(Omega(n^1),?)
4.61/2.27	
4.61/2.27	
4.61/2.27	----------------------------------------
4.61/2.27	
4.61/2.27	(4)
4.61/2.27	BOUNDS(n^1, INF)
4.61/2.28	EOF