4.86/2.40	WORST_CASE(Omega(n^2), O(n^2))
4.94/2.40	proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
4.94/2.40	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
4.94/2.40	
4.94/2.40	
4.94/2.40	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
4.94/2.40	
4.94/2.40	(0) CpxIntTrs
4.94/2.40	(1) Koat Proof [FINISHED, 125 ms]
4.94/2.40	(2) BOUNDS(1, n^2)
4.94/2.40	(3) Loat Proof [FINISHED, 590 ms]
4.94/2.40	(4) BOUNDS(n^2, INF)
4.94/2.40	
4.94/2.40	
4.94/2.40	----------------------------------------
4.94/2.40	
4.94/2.40	(0)
4.94/2.40	Obligation:
4.94/2.40	Complexity Int TRS consisting of the following rules:
4.94/2.40	evalNestedMultipleDepstart(A, B, C, D, E) -> Com_1(evalNestedMultipleDepentryin(A, B, C, D, E)) :|: TRUE
4.94/2.40	evalNestedMultipleDepentryin(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbb3in(0, B, C, D, E)) :|: TRUE
4.94/2.40	evalNestedMultipleDepbb3in(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbbin(A, B, C, D, E)) :|: B >= A + 1
4.94/2.40	evalNestedMultipleDepbb3in(A, B, C, D, E) -> Com_1(evalNestedMultipleDepreturnin(A, B, C, D, E)) :|: A >= B
4.94/2.40	evalNestedMultipleDepbbin(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbb2in(A, B, A + 1, 0, E)) :|: TRUE
4.94/2.40	evalNestedMultipleDepbb2in(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbb1in(A, B, C, D, E)) :|: E >= D + 1
4.94/2.40	evalNestedMultipleDepbb2in(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbb3in(C, B, C, D, E)) :|: D >= E
4.94/2.40	evalNestedMultipleDepbb1in(A, B, C, D, E) -> Com_1(evalNestedMultipleDepbb2in(A, B, C, D + 1, E)) :|: TRUE
4.94/2.40	evalNestedMultipleDepreturnin(A, B, C, D, E) -> Com_1(evalNestedMultipleDepstop(A, B, C, D, E)) :|: TRUE
4.94/2.40	
4.94/2.40	The start-symbols are:[evalNestedMultipleDepstart_5]
4.94/2.40	
4.94/2.40	
4.94/2.40	----------------------------------------
4.94/2.40	
4.94/2.40	(1) Koat Proof (FINISHED)
4.94/2.40	YES(?, 5*ar_1 + 2*ar_1*ar_4 + 6)
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	Initial complexity problem:
4.94/2.40	
4.94/2.40	1:	T:
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.40	
4.94/2.40		start location:	koat_start
4.94/2.40	
4.94/2.40		leaf cost:	0
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	Repeatedly propagating knowledge in problem 1 produces the following problem:
4.94/2.40	
4.94/2.40	2:	T:
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)    evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)    evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.40	
4.94/2.40		start location:	koat_start
4.94/2.40	
4.94/2.40		leaf cost:	0
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	A polynomial rank function with
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepstart) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepentryin) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb3in) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbbin) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepreturnin) = 1
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb2in) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb1in) = 2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepstop) = 0
4.94/2.40	
4.94/2.40		Pol(koat_start) = 2
4.94/2.40	
4.94/2.40	orients all transitions weakly and the transitions
4.94/2.40	
4.94/2.40		evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40		evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40	strictly and produces the following problem:
4.94/2.40	
4.94/2.40	3:	T:
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)    evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)    evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)    evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)    evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.40	
4.94/2.40		start location:	koat_start
4.94/2.40	
4.94/2.40		leaf cost:	0
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	A polynomial rank function with
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepstart) = V_2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepentryin) = V_2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb3in) = -V_1 + V_2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbbin) = -V_1 + V_2 - 1
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepreturnin) = -V_1 + V_2
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb2in) = V_2 - V_3
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb1in) = V_2 - V_3
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepstop) = -V_1 + V_2
4.94/2.40	
4.94/2.40		Pol(koat_start) = V_2
4.94/2.40	
4.94/2.40	orients all transitions weakly and the transition
4.94/2.40	
4.94/2.40		evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40	strictly and produces the following problem:
4.94/2.40	
4.94/2.40	4:	T:
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)       evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)       evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)       evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)       evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.40	
4.94/2.40		start location:	koat_start
4.94/2.40	
4.94/2.40		leaf cost:	0
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	Repeatedly propagating knowledge in problem 4 produces the following problem:
4.94/2.40	
4.94/2.40	5:	T:
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)       evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 1)       evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)       evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.40	
4.94/2.40			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.40	
4.94/2.40			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 2, Cost: 1)       evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.40	
4.94/2.40			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.40	
4.94/2.40		start location:	koat_start
4.94/2.40	
4.94/2.40		leaf cost:	0
4.94/2.40	
4.94/2.40	
4.94/2.40	
4.94/2.40	A polynomial rank function with
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb2in) = 1
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb3in) = 0
4.94/2.40	
4.94/2.40		Pol(evalNestedMultipleDepbb1in) = 1
4.94/2.40	
4.94/2.40	and size complexities
4.94/2.40	
4.94/2.40		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.94/2.40	
4.94/2.40		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.94/2.40	
4.94/2.40		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.94/2.40	
4.94/2.40		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_1 + ar_2
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-2) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-3) = ?
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-2) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-3) = ?
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-2) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-3) = ?
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-2) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-3) = 0
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ar_1 + ar_2
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ?
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = ar_4
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1 + ar_2
4.94/2.40	
4.94/2.40		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 0
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41	orients the transitions
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.41	
4.94/2.41	weakly and the transition
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.41	
4.94/2.41	strictly and produces the following problem:
4.94/2.41	
4.94/2.41	6:	T:
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)       evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)       evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)       evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.41	
4.94/2.41			(Comp: ?, Cost: 1)       evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)       evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.41	
4.94/2.41		start location:	koat_start
4.94/2.41	
4.94/2.41		leaf cost:	0
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	A polynomial rank function with
4.94/2.41	
4.94/2.41		Pol(evalNestedMultipleDepbb2in) = -V_4 + V_5 + 1
4.94/2.41	
4.94/2.41		Pol(evalNestedMultipleDepbb1in) = -V_4 + V_5
4.94/2.41	
4.94/2.41	and size complexities
4.94/2.41	
4.94/2.41		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0
4.94/2.41	
4.94/2.41		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2
4.94/2.41	
4.94/2.41		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3
4.94/2.41	
4.94/2.41		S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_1 + ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-2) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-2) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-2) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-2) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-3) = 0
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-2) = ar_1 + ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ar_1 + ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-0) = 0
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3
4.94/2.41	
4.94/2.41		S("evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4
4.94/2.41	
4.94/2.41	orients the transitions
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.41	
4.94/2.41	weakly and the transition
4.94/2.41	
4.94/2.41		evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41	strictly and produces the following problem:
4.94/2.41	
4.94/2.41	7:	T:
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)                   evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)                   evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)                   evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ar_1*ar_4 + ar_1, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.41	
4.94/2.41			(Comp: ?, Cost: 1)                   evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)                   evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 0)                   koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.41	
4.94/2.41		start location:	koat_start
4.94/2.41	
4.94/2.41		leaf cost:	0
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Repeatedly propagating knowledge in problem 7 produces the following problem:
4.94/2.41	
4.94/2.41	8:	T:
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)                   evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 1)                   evalNestedMultipleDepentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= ar_0 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)                   evalNestedMultipleDepbb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbbin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_0 + 1, 0, ar_4))
4.94/2.41	
4.94/2.41			(Comp: ar_1*ar_4 + ar_1, Cost: 1)    evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_3 + 1 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1, Cost: 1)                evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb3in(ar_2, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_4 ]
4.94/2.41	
4.94/2.41			(Comp: ar_1*ar_4 + ar_1, Cost: 1)    evalNestedMultipleDepbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepbb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 2, Cost: 1)                   evalNestedMultipleDepreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstop(ar_0, ar_1, ar_2, ar_3, ar_4))
4.94/2.41	
4.94/2.41			(Comp: 1, Cost: 0)                   koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalNestedMultipleDepstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]
4.94/2.41	
4.94/2.41		start location:	koat_start
4.94/2.41	
4.94/2.41		leaf cost:	0
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Complexity upper bound 5*ar_1 + 2*ar_1*ar_4 + 6
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Time: 0.123 sec (SMT: 0.102 sec)
4.94/2.41	
4.94/2.41	
4.94/2.41	----------------------------------------
4.94/2.41	
4.94/2.41	(2)
4.94/2.41	BOUNDS(1, n^2)
4.94/2.41	
4.94/2.41	----------------------------------------
4.94/2.41	
4.94/2.41	(3) Loat Proof (FINISHED)
4.94/2.41	
4.94/2.41	
4.94/2.41	### Pre-processing the ITS problem ###
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Initial linear ITS problem
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      0: evalNestedMultipleDepstart -> evalNestedMultipleDepentryin : [], cost: 1
4.94/2.41	
4.94/2.41	      1: evalNestedMultipleDepentryin -> evalNestedMultipleDepbb3in : A'=0, [], cost: 1
4.94/2.41	
4.94/2.41	      2: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbbin : [ B>=1+A ], cost: 1
4.94/2.41	
4.94/2.41	      3: evalNestedMultipleDepbb3in -> evalNestedMultipleDepreturnin : [ A>=B ], cost: 1
4.94/2.41	
4.94/2.41	      4: evalNestedMultipleDepbbin -> evalNestedMultipleDepbb2in : C'=1+A, D'=0, [], cost: 1
4.94/2.41	
4.94/2.41	      5: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb1in : [ E>=1+D ], cost: 1
4.94/2.41	
4.94/2.41	      6: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb3in : A'=C, [ D>=E ], cost: 1
4.94/2.41	
4.94/2.41	      7: evalNestedMultipleDepbb1in -> evalNestedMultipleDepbb2in : D'=1+D, [], cost: 1
4.94/2.41	
4.94/2.41	      8: evalNestedMultipleDepreturnin -> evalNestedMultipleDepstop : [], cost: 1
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Removed unreachable and leaf rules:
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      0: evalNestedMultipleDepstart -> evalNestedMultipleDepentryin : [], cost: 1
4.94/2.41	
4.94/2.41	      1: evalNestedMultipleDepentryin -> evalNestedMultipleDepbb3in : A'=0, [], cost: 1
4.94/2.41	
4.94/2.41	      2: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbbin : [ B>=1+A ], cost: 1
4.94/2.41	
4.94/2.41	      4: evalNestedMultipleDepbbin -> evalNestedMultipleDepbb2in : C'=1+A, D'=0, [], cost: 1
4.94/2.41	
4.94/2.41	      5: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb1in : [ E>=1+D ], cost: 1
4.94/2.41	
4.94/2.41	      6: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb3in : A'=C, [ D>=E ], cost: 1
4.94/2.41	
4.94/2.41	      7: evalNestedMultipleDepbb1in -> evalNestedMultipleDepbb2in : D'=1+D, [], cost: 1
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	### Simplification by acceleration and chaining ###
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Eliminated locations (on linear paths):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     10: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb2in : C'=1+A, D'=0, [ B>=1+A ], cost: 2
4.94/2.41	
4.94/2.41	      6: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb3in : A'=C, [ D>=E ], cost: 1
4.94/2.41	
4.94/2.41	     11: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb2in : D'=1+D, [ E>=1+D ], cost: 2
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Accelerating simple loops of location 4.
4.94/2.41	
4.94/2.41	   Accelerating the following rules:
4.94/2.41	
4.94/2.41	     11: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb2in : D'=1+D, [ E>=1+D ], cost: 2
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	   Accelerated rule 11 with metering function -D+E, yielding the new rule 12.
4.94/2.41	
4.94/2.41	   Removing the simple loops: 11.
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Accelerated all simple loops using metering functions (where possible):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     10: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb2in : C'=1+A, D'=0, [ B>=1+A ], cost: 2
4.94/2.41	
4.94/2.41	      6: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb3in : A'=C, [ D>=E ], cost: 1
4.94/2.41	
4.94/2.41	     12: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb2in : D'=E, [ E>=1+D ], cost: -2*D+2*E
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Chained accelerated rules (with incoming rules):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     10: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb2in : C'=1+A, D'=0, [ B>=1+A ], cost: 2
4.94/2.41	
4.94/2.41	     13: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb2in : C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 2+2*E
4.94/2.41	
4.94/2.41	      6: evalNestedMultipleDepbb2in -> evalNestedMultipleDepbb3in : A'=C, [ D>=E ], cost: 1
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Eliminated locations (on tree-shaped paths):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     14: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=1+A, C'=1+A, D'=0, [ B>=1+A && 0>=E ], cost: 3
4.94/2.41	
4.94/2.41	     15: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=1+A, C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 3+2*E
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Accelerating simple loops of location 2.
4.94/2.41	
4.94/2.41	   Accelerating the following rules:
4.94/2.41	
4.94/2.41	     14: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=1+A, C'=1+A, D'=0, [ B>=1+A && 0>=E ], cost: 3
4.94/2.41	
4.94/2.41	     15: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=1+A, C'=1+A, D'=E, [ B>=1+A && E>=1 ], cost: 3+2*E
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	   Accelerated rule 14 with metering function -A+B, yielding the new rule 16.
4.94/2.41	
4.94/2.41	   Accelerated rule 15 with metering function -A+B, yielding the new rule 17.
4.94/2.41	
4.94/2.41	   Removing the simple loops: 14 15.
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Accelerated all simple loops using metering functions (where possible):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     16: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=0, [ B>=1+A && 0>=E ], cost: -3*A+3*B
4.94/2.41	
4.94/2.41	     17: evalNestedMultipleDepbb3in -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=E, [ B>=1+A && E>=1 ], cost: -3*A-2*E*(A-B)+3*B
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Chained accelerated rules (with incoming rules):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	      9: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=0, [], cost: 2
4.94/2.41	
4.94/2.41	     18: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 2+3*B
4.94/2.41	
4.94/2.41	     19: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 2+2*E*B+3*B
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Removed unreachable locations (and leaf rules with constant cost):
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	     18: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 2+3*B
4.94/2.41	
4.94/2.41	     19: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 2+2*E*B+3*B
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	### Computing asymptotic complexity ###
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Fully simplified ITS problem
4.94/2.41	
4.94/2.41	   Start location: evalNestedMultipleDepstart
4.94/2.41	
4.94/2.41	     18: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=0, [ B>=1 && 0>=E ], cost: 2+3*B
4.94/2.41	
4.94/2.41	     19: evalNestedMultipleDepstart -> evalNestedMultipleDepbb3in : A'=B, C'=B, D'=E, [ B>=1 && E>=1 ], cost: 2+2*E*B+3*B
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Computing asymptotic complexity for rule 18
4.94/2.41	
4.94/2.41	   Solved the limit problem by the following transformations:
4.94/2.41	
4.94/2.41	      Created initial limit problem:
4.94/2.41	
4.94/2.41	      2+3*B (+), 1-E (+/+!), B (+/+!) [not solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	      removing all constraints (solved by SMT)
4.94/2.41	
4.94/2.41	      resulting limit problem: [solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	      applying transformation rule (C) using substitution {E==-n,B==n}
4.94/2.41	
4.94/2.41	      resulting limit problem:
4.94/2.41	
4.94/2.41	      [solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	   Solution:
4.94/2.41	
4.94/2.41	      E / -n
4.94/2.41	
4.94/2.41	      B / n
4.94/2.41	
4.94/2.41	   Resulting cost 2+3*n has complexity: Poly(n^1)
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Found new complexity Poly(n^1).
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Computing asymptotic complexity for rule 19
4.94/2.41	
4.94/2.41	   Solved the limit problem by the following transformations:
4.94/2.41	
4.94/2.41	      Created initial limit problem:
4.94/2.41	
4.94/2.41	      2+2*E*B+3*B (+), E (+/+!), B (+/+!) [not solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	      removing all constraints (solved by SMT)
4.94/2.41	
4.94/2.41	      resulting limit problem: [solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	      applying transformation rule (C) using substitution {E==n,B==n}
4.94/2.41	
4.94/2.41	      resulting limit problem:
4.94/2.41	
4.94/2.41	      [solved]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	   Solution:
4.94/2.41	
4.94/2.41	      E / n
4.94/2.41	
4.94/2.41	      B / n
4.94/2.41	
4.94/2.41	   Resulting cost 2+2*n^2+3*n has complexity: Poly(n^2)
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Found new complexity Poly(n^2).
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	Obtained the following overall complexity (w.r.t. the length of the input n):
4.94/2.41	
4.94/2.41	   Complexity:  Poly(n^2)
4.94/2.41	
4.94/2.41	   Cpx degree:  2
4.94/2.41	
4.94/2.41	   Solved cost: 2+2*n^2+3*n
4.94/2.41	
4.94/2.41	   Rule cost:   2+2*E*B+3*B
4.94/2.41	
4.94/2.41	   Rule guard:  [ B>=1 && E>=1 ]
4.94/2.41	
4.94/2.41	
4.94/2.41	
4.94/2.41	WORST_CASE(Omega(n^2),?)
4.94/2.41	
4.94/2.41	
4.94/2.41	----------------------------------------
4.94/2.41	
4.94/2.41	(4)
4.94/2.41	BOUNDS(n^2, INF)
4.97/2.44	EOF