5.66/2.57	WORST_CASE(Omega(n^1), O(n^1))
5.66/2.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
5.66/2.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.66/2.58	
5.66/2.58	
5.66/2.58	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).
5.66/2.58	
5.66/2.58	(0) CpxIntTrs
5.66/2.58	(1) Koat Proof [FINISHED, 336 ms]
5.66/2.58	(2) BOUNDS(1, n^1)
5.66/2.58	(3) Loat Proof [FINISHED, 922 ms]
5.66/2.58	(4) BOUNDS(n^1, INF)
5.66/2.58	
5.66/2.58	
5.66/2.58	----------------------------------------
5.66/2.58	
5.66/2.58	(0)
5.66/2.58	Obligation:
5.66/2.58	Complexity Int TRS consisting of the following rules:
5.66/2.58	evalNestedMultiplestart(A, B, C, D, E) -> Com_1(evalNestedMultipleentryin(A, B, C, D, E)) :|: TRUE
5.66/2.58	evalNestedMultipleentryin(A, B, C, D, E) -> Com_1(evalNestedMultiplebb5in(B, A, D, C, E)) :|: TRUE
5.66/2.58	evalNestedMultiplebb5in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb2in(A, B, C, D, D)) :|: A >= B + 1
5.66/2.58	evalNestedMultiplebb5in(A, B, C, D, E) -> Com_1(evalNestedMultiplereturnin(A, B, C, D, E)) :|: B >= A
5.66/2.58	evalNestedMultiplebb2in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb4in(A, B, C, D, E)) :|: E >= C
5.66/2.58	evalNestedMultiplebb2in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb3in(A, B, C, D, E)) :|: C >= E + 1
5.66/2.58	evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb1in(A, B, C, D, E)) :|: 0 >= F + 1
5.66/2.58	evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb1in(A, B, C, D, E)) :|: F >= 1
5.66/2.58	evalNestedMultiplebb3in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb4in(A, B, C, D, E)) :|: TRUE
5.66/2.58	evalNestedMultiplebb1in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb2in(A, B, C, D, E + 1)) :|: TRUE
5.66/2.58	evalNestedMultiplebb4in(A, B, C, D, E) -> Com_1(evalNestedMultiplebb5in(A, B + 1, C, E, E)) :|: TRUE
5.66/2.58	evalNestedMultiplereturnin(A, B, C, D, E) -> Com_1(evalNestedMultiplestop(A, B, C, D, E)) :|: TRUE
5.66/2.58	
5.66/2.58	The start-symbols are:[evalNestedMultiplestart_5]
5.66/2.58	
5.66/2.58	
5.66/2.58	----------------------------------------
5.66/2.58	
5.66/2.58	(1) Koat Proof (FINISHED)
5.66/2.58	YES(?, 11*ar_0 + 11*ar_1 + 12*ar_2 + 12*ar_3 + 17)
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Initial complexity problem:
5.66/2.58	
5.66/2.58	1:	T:
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.66/2.58	
5.66/2.58	2:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)    evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)    evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	A polynomial rank function with
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestart) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultipleentryin) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb5in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb2in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplereturnin) = 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb4in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb3in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb1in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestop) = 0
5.66/2.58	
5.66/2.58		Pol(koat_start) = 2
5.66/2.58	
5.66/2.58	orients all transitions weakly and the transitions
5.66/2.58	
5.66/2.58		evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58		evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58	strictly and produces the following problem:
5.66/2.58	
5.66/2.58	3:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)    evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)    evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)    evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)    evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	A polynomial rank function with
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestart) = -V_1 + V_2 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultipleentryin) = -V_1 + V_2 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb5in) = V_1 - V_2 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb2in) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplereturnin) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb4in) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb3in) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb1in) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestop) = V_1 - V_2
5.66/2.58	
5.66/2.58		Pol(koat_start) = -V_1 + V_2 + 1
5.66/2.58	
5.66/2.58	orients all transitions weakly and the transition
5.66/2.58	
5.66/2.58		evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58	strictly and produces the following problem:
5.66/2.58	
5.66/2.58	4:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                  evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                  evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 1, Cost: 1)    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                  evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                  evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                  evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)                  koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	A polynomial rank function with
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb4in) = 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb5in) = 0
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb3in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb1in) = 2
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb2in) = 2
5.66/2.58	
5.66/2.58	and size complexities
5.66/2.58	
5.66/2.58		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
5.66/2.58	
5.66/2.58		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
5.66/2.58	
5.66/2.58		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
5.66/2.58	
5.66/2.58		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
5.66/2.58	
5.66/2.58		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
5.66/2.58	
5.66/2.58		S("evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-1) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-3) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]", 0-4) = ?
5.66/2.58	
5.66/2.58		S("evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))", 0-0) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))", 0-1) = ar_0
5.66/2.58	
5.66/2.58		S("evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))", 0-2) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))", 0-3) = ar_2
5.66/2.58	
5.66/2.58		S("evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))", 0-4) = ar_4
5.66/2.58	
5.66/2.58		S("evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
5.66/2.58	
5.66/2.58		S("evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
5.66/2.58	
5.66/2.58		S("evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
5.66/2.58	
5.66/2.58		S("evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
5.66/2.58	
5.66/2.58		S("evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
5.66/2.58	
5.66/2.58	orients the transitions
5.66/2.58	
5.66/2.58		evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58	weakly and the transitions
5.66/2.58	
5.66/2.58		evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58		evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58	strictly and produces the following problem:
5.66/2.58	
5.66/2.58	5:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                      evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                      evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 1, Cost: 1)        evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                      evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1))
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                      evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Applied AI with 'oct' on problem 5 to obtain the following invariants:
5.66/2.58	
5.66/2.58	  For symbol evalNestedMultiplebb1in: X_3 - X_5 - 1 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
5.66/2.58	
5.66/2.58	  For symbol evalNestedMultiplebb2in: -X_4 + X_5 >= 0 /\ X_1 - X_2 - 1 >= 0
5.66/2.58	
5.66/2.58	  For symbol evalNestedMultiplebb3in: X_3 - X_5 - 1 >= 0 /\ -X_4 + X_5 >= 0 /\ X_3 - X_4 - 1 >= 0 /\ X_1 - X_2 - 1 >= 0
5.66/2.58	
5.66/2.58	  For symbol evalNestedMultiplebb4in: -X_4 + X_5 >= 0 /\ X_1 - X_2 - 1 >= 0
5.66/2.58	
5.66/2.58	  For symbol evalNestedMultiplereturnin: -X_1 + X_2 >= 0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	This yielded the following problem:
5.66/2.58	
5.66/2.58	6:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)                      koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                      evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 + ar_1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ?, Cost: 1)                      evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                      evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 1, Cost: 1)        evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                      evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                      evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	A polynomial rank function with
5.66/2.58	
5.66/2.58		Pol(koat_start) = -V_1 + V_2 - 3*V_3 + 3*V_4 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestart) = -V_1 + V_2 - 3*V_3 + 3*V_4 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplereturnin) = V_1 - V_2 + 3*V_3 - 3*V_4
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplestop) = V_1 - V_2 + 3*V_3 - 3*V_4
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb4in) = V_1 - V_2 + 3*V_3 - 3*V_5
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb5in) = V_1 - V_2 + 3*V_3 - 3*V_4 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb1in) = V_1 - V_2 + 3*V_3 - 3*V_5 - 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb2in) = V_1 - V_2 + 3*V_3 - 3*V_5 + 1
5.66/2.58	
5.66/2.58		Pol(evalNestedMultiplebb3in) = V_1 - V_2 + 3*V_3 - 3*V_5
5.66/2.58	
5.66/2.58		Pol(evalNestedMultipleentryin) = -V_1 + V_2 - 3*V_3 + 3*V_4 + 1
5.66/2.58	
5.66/2.58	orients all transitions weakly and the transitions
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ f >= 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58		evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58	strictly and produces the following problem:
5.66/2.58	
5.66/2.58	7:	T:
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 0)                                    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                                    evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplestop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_0 + ar_1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)                  evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_0, ar_1 + 1, ar_2, ar_4, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 3*ar_2 + 3*ar_3 + 1, Cost: 1)    evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4 + 1)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)                  evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 3*ar_2 + 3*ar_3 + 1, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ f >= 1 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 3*ar_2 + 3*ar_3 + 1, Cost: 1)    evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 - ar_4 - 1 >= 0 /\ -ar_3 + ar_4 >= 0 /\ ar_2 - ar_3 - 1 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ 0 >= f + 1 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 3*ar_2 + 3*ar_3 + 1, Cost: 1)    evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_2 >= ar_4 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 2*ar_0 + 2*ar_1 + 2, Cost: 1)                  evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb4in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_3 + ar_4 >= 0 /\ ar_0 - ar_1 - 1 >= 0 /\ ar_4 >= ar_2 ]
5.66/2.58	
5.66/2.58			(Comp: 2, Cost: 1)                                    evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplereturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 ]
5.66/2.58	
5.66/2.58			(Comp: ar_0 + ar_1 + 1, Cost: 1)                      evalNestedMultiplebb5in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb2in(ar_0, ar_1, ar_2, ar_3, ar_3)) [ ar_0 >= ar_1 + 1 ]
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                                    evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultiplebb5in(ar_1, ar_0, ar_3, ar_2, ar_4))
5.66/2.58	
5.66/2.58			(Comp: 1, Cost: 1)                                    evalNestedMultiplestart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
5.66/2.58	
5.66/2.58		start location:	koat_start
5.66/2.58	
5.66/2.58		leaf cost:	0
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Complexity upper bound 11*ar_0 + 11*ar_1 + 12*ar_2 + 12*ar_3 + 17
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Time: 0.339 sec (SMT: 0.259 sec)
5.66/2.58	
5.66/2.58	
5.66/2.58	----------------------------------------
5.66/2.58	
5.66/2.58	(2)
5.66/2.58	BOUNDS(1, n^1)
5.66/2.58	
5.66/2.58	----------------------------------------
5.66/2.58	
5.66/2.58	(3) Loat Proof (FINISHED)
5.66/2.58	
5.66/2.58	
5.66/2.58	### Pre-processing the ITS problem ###
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Initial linear ITS problem
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	      0: evalNestedMultiplestart -> evalNestedMultipleentryin : [], cost: 1
5.66/2.58	
5.66/2.58	      1: evalNestedMultipleentryin -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 1
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.58	
5.66/2.58	      3: evalNestedMultiplebb5in -> evalNestedMultiplereturnin : [ B>=A ], cost: 1
5.66/2.58	
5.66/2.58	      4: evalNestedMultiplebb2in -> evalNestedMultiplebb4in : [ E>=C ], cost: 1
5.66/2.58	
5.66/2.58	      5: evalNestedMultiplebb2in -> evalNestedMultiplebb3in : [ C>=1+E ], cost: 1
5.66/2.58	
5.66/2.58	      6: evalNestedMultiplebb3in -> evalNestedMultiplebb1in : [ 0>=1+free ], cost: 1
5.66/2.58	
5.66/2.58	      7: evalNestedMultiplebb3in -> evalNestedMultiplebb1in : [ free_1>=1 ], cost: 1
5.66/2.58	
5.66/2.58	      8: evalNestedMultiplebb3in -> evalNestedMultiplebb4in : [], cost: 1
5.66/2.58	
5.66/2.58	      9: evalNestedMultiplebb1in -> evalNestedMultiplebb2in : E'=1+E, [], cost: 1
5.66/2.58	
5.66/2.58	     10: evalNestedMultiplebb4in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [], cost: 1
5.66/2.58	
5.66/2.58	     11: evalNestedMultiplereturnin -> evalNestedMultiplestop : [], cost: 1
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Removed unreachable and leaf rules:
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	      0: evalNestedMultiplestart -> evalNestedMultipleentryin : [], cost: 1
5.66/2.58	
5.66/2.58	      1: evalNestedMultipleentryin -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 1
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.58	
5.66/2.58	      4: evalNestedMultiplebb2in -> evalNestedMultiplebb4in : [ E>=C ], cost: 1
5.66/2.58	
5.66/2.58	      5: evalNestedMultiplebb2in -> evalNestedMultiplebb3in : [ C>=1+E ], cost: 1
5.66/2.58	
5.66/2.58	      6: evalNestedMultiplebb3in -> evalNestedMultiplebb1in : [ 0>=1+free ], cost: 1
5.66/2.58	
5.66/2.58	      7: evalNestedMultiplebb3in -> evalNestedMultiplebb1in : [ free_1>=1 ], cost: 1
5.66/2.58	
5.66/2.58	      8: evalNestedMultiplebb3in -> evalNestedMultiplebb4in : [], cost: 1
5.66/2.58	
5.66/2.58	      9: evalNestedMultiplebb1in -> evalNestedMultiplebb2in : E'=1+E, [], cost: 1
5.66/2.58	
5.66/2.58	     10: evalNestedMultiplebb4in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [], cost: 1
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Simplified all rules, resulting in:
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	      0: evalNestedMultiplestart -> evalNestedMultipleentryin : [], cost: 1
5.66/2.58	
5.66/2.58	      1: evalNestedMultipleentryin -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 1
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.58	
5.66/2.58	      4: evalNestedMultiplebb2in -> evalNestedMultiplebb4in : [ E>=C ], cost: 1
5.66/2.58	
5.66/2.58	      5: evalNestedMultiplebb2in -> evalNestedMultiplebb3in : [ C>=1+E ], cost: 1
5.66/2.58	
5.66/2.58	      7: evalNestedMultiplebb3in -> evalNestedMultiplebb1in : [], cost: 1
5.66/2.58	
5.66/2.58	      8: evalNestedMultiplebb3in -> evalNestedMultiplebb4in : [], cost: 1
5.66/2.58	
5.66/2.58	      9: evalNestedMultiplebb1in -> evalNestedMultiplebb2in : E'=1+E, [], cost: 1
5.66/2.58	
5.66/2.58	     10: evalNestedMultiplebb4in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [], cost: 1
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	### Simplification by acceleration and chaining ###
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Eliminated locations (on linear paths):
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.58	
5.66/2.58	      4: evalNestedMultiplebb2in -> evalNestedMultiplebb4in : [ E>=C ], cost: 1
5.66/2.58	
5.66/2.58	      5: evalNestedMultiplebb2in -> evalNestedMultiplebb3in : [ C>=1+E ], cost: 1
5.66/2.58	
5.66/2.58	      8: evalNestedMultiplebb3in -> evalNestedMultiplebb4in : [], cost: 1
5.66/2.58	
5.66/2.58	     13: evalNestedMultiplebb3in -> evalNestedMultiplebb2in : E'=1+E, [], cost: 2
5.66/2.58	
5.66/2.58	     10: evalNestedMultiplebb4in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [], cost: 1
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Eliminated locations (on tree-shaped paths):
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.58	
5.66/2.58	     15: evalNestedMultiplebb2in -> evalNestedMultiplebb2in : E'=1+E, [ C>=1+E ], cost: 3
5.66/2.58	
5.66/2.58	     16: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ E>=C ], cost: 2
5.66/2.58	
5.66/2.58	     17: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ C>=1+E ], cost: 3
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Accelerating simple loops of location 3.
5.66/2.58	
5.66/2.58	   Accelerating the following rules:
5.66/2.58	
5.66/2.58	     15: evalNestedMultiplebb2in -> evalNestedMultiplebb2in : E'=1+E, [ C>=1+E ], cost: 3
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	   Accelerated rule 15 with metering function C-E, yielding the new rule 18.
5.66/2.58	
5.66/2.58	   Removing the simple loops: 15.
5.66/2.58	
5.66/2.58	
5.66/2.58	
5.66/2.58	Accelerated all simple loops using metering functions (where possible):
5.66/2.58	
5.66/2.58	   Start location: evalNestedMultiplestart
5.66/2.58	
5.66/2.58	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.58	
5.66/2.58	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.59	
5.66/2.59	     16: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ E>=C ], cost: 2
5.66/2.59	
5.66/2.59	     17: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ C>=1+E ], cost: 3
5.66/2.59	
5.66/2.59	     18: evalNestedMultiplebb2in -> evalNestedMultiplebb2in : E'=C, [ C>=1+E ], cost: 3*C-3*E
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Chained accelerated rules (with incoming rules):
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.59	
5.66/2.59	      2: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=D, [ A>=1+B ], cost: 1
5.66/2.59	
5.66/2.59	     19: evalNestedMultiplebb5in -> evalNestedMultiplebb2in : E'=C, [ A>=1+B && C>=1+D ], cost: 1+3*C-3*D
5.66/2.59	
5.66/2.59	     16: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ E>=C ], cost: 2
5.66/2.59	
5.66/2.59	     17: evalNestedMultiplebb2in -> evalNestedMultiplebb5in : B'=1+B, D'=E, [ C>=1+E ], cost: 3
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Eliminated locations (on tree-shaped paths):
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.59	
5.66/2.59	     20: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, D'=D, E'=D, [ A>=1+B && D>=C ], cost: 3
5.66/2.59	
5.66/2.59	     21: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, D'=D, E'=D, [ A>=1+B && C>=1+D ], cost: 4
5.66/2.59	
5.66/2.59	     22: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, D'=C, E'=C, [ A>=1+B && C>=1+D ], cost: 3+3*C-3*D
5.66/2.59	
5.66/2.59	     23: evalNestedMultiplebb5in -> [10] : [ A>=1+B && C>=1+D ], cost: 1+3*C-3*D
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Accelerating simple loops of location 2.
5.66/2.59	
5.66/2.59	   Simplified some of the simple loops (and removed duplicate rules).
5.66/2.59	
5.66/2.59	   Accelerating the following rules:
5.66/2.59	
5.66/2.59	     20: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, E'=D, [ A>=1+B && D>=C ], cost: 3
5.66/2.59	
5.66/2.59	     21: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, E'=D, [ A>=1+B && C>=1+D ], cost: 4
5.66/2.59	
5.66/2.59	     22: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, D'=C, E'=C, [ A>=1+B && C>=1+D ], cost: 3+3*C-3*D
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	   Accelerated rule 20 with metering function A-B, yielding the new rule 24.
5.66/2.59	
5.66/2.59	   Accelerated rule 21 with metering function A-B, yielding the new rule 25.
5.66/2.59	
5.66/2.59	   Found no metering function for rule 22.
5.66/2.59	
5.66/2.59	   Removing the simple loops: 20 21.
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Accelerated all simple loops using metering functions (where possible):
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.59	
5.66/2.59	     22: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=1+B, D'=C, E'=C, [ A>=1+B && C>=1+D ], cost: 3+3*C-3*D
5.66/2.59	
5.66/2.59	     23: evalNestedMultiplebb5in -> [10] : [ A>=1+B && C>=1+D ], cost: 1+3*C-3*D
5.66/2.59	
5.66/2.59	     24: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=A, E'=D, [ A>=1+B && D>=C ], cost: 3*A-3*B
5.66/2.59	
5.66/2.59	     25: evalNestedMultiplebb5in -> evalNestedMultiplebb5in : B'=A, E'=D, [ A>=1+B && C>=1+D ], cost: 4*A-4*B
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Chained accelerated rules (with incoming rules):
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     12: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=A, C'=D, D'=C, [], cost: 2
5.66/2.59	
5.66/2.59	     26: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, B'=1+A, C'=D, E'=D, [ B>=1+A && D>=1+C ], cost: 5-3*C+3*D
5.66/2.59	
5.66/2.59	     27: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, C'=D, D'=C, E'=C, [ B>=1+A && C>=D ], cost: 2-3*A+3*B
5.66/2.59	
5.66/2.59	     28: evalNestedMultiplestart -> evalNestedMultiplebb5in : A'=B, C'=D, D'=C, E'=C, [ B>=1+A && D>=1+C ], cost: 2-4*A+4*B
5.66/2.59	
5.66/2.59	     23: evalNestedMultiplebb5in -> [10] : [ A>=1+B && C>=1+D ], cost: 1+3*C-3*D
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Eliminated locations (on tree-shaped paths):
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     29: evalNestedMultiplestart -> [10] : A'=B, B'=A, C'=D, D'=C, [ B>=1+A && D>=1+C ], cost: 3-3*C+3*D
5.66/2.59	
5.66/2.59	     30: evalNestedMultiplestart -> [12] : [ B>=1+A && D>=1+C ], cost: 5-3*C+3*D
5.66/2.59	
5.66/2.59	     31: evalNestedMultiplestart -> [12] : [ B>=1+A && C>=D ], cost: 2-3*A+3*B
5.66/2.59	
5.66/2.59	     32: evalNestedMultiplestart -> [12] : [ B>=1+A && D>=1+C ], cost: 2-4*A+4*B
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	### Computing asymptotic complexity ###
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Fully simplified ITS problem
5.66/2.59	
5.66/2.59	   Start location: evalNestedMultiplestart
5.66/2.59	
5.66/2.59	     30: evalNestedMultiplestart -> [12] : [ B>=1+A && D>=1+C ], cost: 5-3*C+3*D
5.66/2.59	
5.66/2.59	     31: evalNestedMultiplestart -> [12] : [ B>=1+A && C>=D ], cost: 2-3*A+3*B
5.66/2.59	
5.66/2.59	     32: evalNestedMultiplestart -> [12] : [ B>=1+A && D>=1+C ], cost: 2-4*A+4*B
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Computing asymptotic complexity for rule 30
5.66/2.59	
5.66/2.59	   Solved the limit problem by the following transformations:
5.66/2.59	
5.66/2.59	      Created initial limit problem:
5.66/2.59	
5.66/2.59	      -A+B (+/+!), 5-3*C+3*D (+), -C+D (+/+!) [not solved]
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	      removing all constraints (solved by SMT)
5.66/2.59	
5.66/2.59	      resulting limit problem: [solved]
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	      applying transformation rule (C) using substitution {C==0,D==n,A==-1,B==0}
5.66/2.59	
5.66/2.59	      resulting limit problem:
5.66/2.59	
5.66/2.59	      [solved]
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	   Solution:
5.66/2.59	
5.66/2.59	      C / 0
5.66/2.59	
5.66/2.59	      D / n
5.66/2.59	
5.66/2.59	      A / -1
5.66/2.59	
5.66/2.59	      B / 0
5.66/2.59	
5.66/2.59	   Resulting cost 5+3*n has complexity: Poly(n^1)
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Found new complexity Poly(n^1).
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	Obtained the following overall complexity (w.r.t. the length of the input n):
5.66/2.59	
5.66/2.59	   Complexity:  Poly(n^1)
5.66/2.59	
5.66/2.59	   Cpx degree:  1
5.66/2.59	
5.66/2.59	   Solved cost: 5+3*n
5.66/2.59	
5.66/2.59	   Rule cost:   5-3*C+3*D
5.66/2.59	
5.66/2.59	   Rule guard:  [ B>=1+A && D>=1+C ]
5.66/2.59	
5.66/2.59	
5.66/2.59	
5.66/2.59	WORST_CASE(Omega(n^1),?)
5.66/2.59	
5.66/2.59	
5.66/2.59	----------------------------------------
5.66/2.59	
5.66/2.59	(4)
5.66/2.59	BOUNDS(n^1, INF)
5.78/2.61	EOF