5.90/2.73	WORST_CASE(Omega(n^2), O(n^2))
5.90/2.74	proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
5.90/2.74	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.90/2.74	
5.90/2.74	
5.90/2.74	The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^2, n^2).
5.90/2.74	
5.90/2.74	(0) CpxIntTrs
5.90/2.74	(1) Koat Proof [FINISHED, 113 ms]
5.90/2.74	(2) BOUNDS(1, n^2)
5.90/2.74	(3) Loat Proof [FINISHED, 1129 ms]
5.90/2.74	(4) BOUNDS(n^2, INF)
5.90/2.74	
5.90/2.74	
5.90/2.74	----------------------------------------
5.90/2.74	
5.90/2.74	(0)
5.90/2.74	Obligation:
5.90/2.74	Complexity Int TRS consisting of the following rules:
5.90/2.74	evalinsertsortstart(A, B, C, D) -> Com_1(evalinsertsortentryin(A, B, C, D)) :|: TRUE
5.90/2.74	evalinsertsortentryin(A, B, C, D) -> Com_1(evalinsertsortbb5in(1, B, C, D)) :|: TRUE
5.90/2.74	evalinsertsortbb5in(A, B, C, D) -> Com_1(evalinsertsortbbin(A, B, C, D)) :|: B >= A + 1
5.90/2.74	evalinsertsortbb5in(A, B, C, D) -> Com_1(evalinsertsortreturnin(A, B, C, D)) :|: A >= B
5.90/2.74	evalinsertsortbbin(A, B, C, D) -> Com_1(evalinsertsortbb2in(A, B, E, A - 1)) :|: TRUE
5.90/2.74	evalinsertsortbb2in(A, B, C, D) -> Com_1(evalinsertsortbb4in(A, B, C, D)) :|: 0 >= D + 1
5.90/2.74	evalinsertsortbb2in(A, B, C, D) -> Com_1(evalinsertsortbb3in(A, B, C, D)) :|: D >= 0
5.90/2.74	evalinsertsortbb3in(A, B, C, D) -> Com_1(evalinsertsortbb1in(A, B, C, D)) :|: E >= C + 1
5.90/2.74	evalinsertsortbb3in(A, B, C, D) -> Com_1(evalinsertsortbb4in(A, B, C, D)) :|: C >= E
5.90/2.74	evalinsertsortbb1in(A, B, C, D) -> Com_1(evalinsertsortbb2in(A, B, C, D - 1)) :|: TRUE
5.90/2.74	evalinsertsortbb4in(A, B, C, D) -> Com_1(evalinsertsortbb5in(A + 1, B, C, D)) :|: TRUE
5.90/2.74	evalinsertsortreturnin(A, B, C, D) -> Com_1(evalinsertsortstop(A, B, C, D)) :|: TRUE
5.90/2.74	
5.90/2.74	The start-symbols are:[evalinsertsortstart_4]
5.90/2.74	
5.90/2.74	
5.90/2.74	----------------------------------------
5.90/2.74	
5.90/2.74	(1) Koat Proof (FINISHED)
5.90/2.74	YES(?, 41*ar_1 + 6*ar_1^2 + 6)
5.90/2.74	
5.90/2.74	
5.90/2.74	
5.90/2.74	Initial complexity problem:
5.90/2.74	
5.90/2.74	1:	T:
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.74	
5.90/2.74		start location:	koat_start
5.90/2.74	
5.90/2.74		leaf cost:	0
5.90/2.74	
5.90/2.74	
5.90/2.74	
5.90/2.74	Repeatedly propagating knowledge in problem 1 produces the following problem:
5.90/2.74	
5.90/2.74	2:	T:
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)    evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)    evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.74	
5.90/2.74		start location:	koat_start
5.90/2.74	
5.90/2.74		leaf cost:	0
5.90/2.74	
5.90/2.74	
5.90/2.74	
5.90/2.74	A polynomial rank function with
5.90/2.74	
5.90/2.74		Pol(evalinsertsortstart) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortentryin) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb5in) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbbin) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortreturnin) = 1
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb2in) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb4in) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb3in) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb1in) = 2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortstop) = 0
5.90/2.74	
5.90/2.74		Pol(koat_start) = 2
5.90/2.74	
5.90/2.74	orients all transitions weakly and the transitions
5.90/2.74	
5.90/2.74		evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74		evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74	strictly and produces the following problem:
5.90/2.74	
5.90/2.74	3:	T:
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)    evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)    evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: 2, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)    evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 2, Cost: 1)    evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.74	
5.90/2.74		start location:	koat_start
5.90/2.74	
5.90/2.74		leaf cost:	0
5.90/2.74	
5.90/2.74	
5.90/2.74	
5.90/2.74	A polynomial rank function with
5.90/2.74	
5.90/2.74		Pol(evalinsertsortstart) = V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortentryin) = V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb5in) = -V_1 + V_2 + 1
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbbin) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortreturnin) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb2in) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb4in) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb3in) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortbb1in) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(evalinsertsortstop) = -V_1 + V_2
5.90/2.74	
5.90/2.74		Pol(koat_start) = V_2
5.90/2.74	
5.90/2.74	orients all transitions weakly and the transition
5.90/2.74	
5.90/2.74		evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74	strictly and produces the following problem:
5.90/2.74	
5.90/2.74	4:	T:
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)       evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)       evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ar_1, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: 2, Cost: 1)       evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 2, Cost: 1)       evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.74	
5.90/2.74		start location:	koat_start
5.90/2.74	
5.90/2.74		leaf cost:	0
5.90/2.74	
5.90/2.74	
5.90/2.74	
5.90/2.74	Repeatedly propagating knowledge in problem 4 produces the following problem:
5.90/2.74	
5.90/2.74	5:	T:
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)       evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: 1, Cost: 1)       evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.74	
5.90/2.74			(Comp: ar_1, Cost: 1)    evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: 2, Cost: 1)       evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.74	
5.90/2.74			(Comp: ar_1, Cost: 1)    evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.74	
5.90/2.74			(Comp: ?, Cost: 1)       evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)       evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)       evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)       evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)       evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)       evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 0)       koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.75	
5.90/2.75		start location:	koat_start
5.90/2.75	
5.90/2.75		leaf cost:	0
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	A polynomial rank function with
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb4in) = 1
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb5in) = 0
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb3in) = 2
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb1in) = 2
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb2in) = 2
5.90/2.75	
5.90/2.75	and size complexities
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-0) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-0) = 1
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.90/2.75	
5.90/2.75	orients the transitions
5.90/2.75	
5.90/2.75		evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75		evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75		evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75		evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.75	
5.90/2.75		evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75		evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75	weakly and the transitions
5.90/2.75	
5.90/2.75		evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75		evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75		evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.75	
5.90/2.75	strictly and produces the following problem:
5.90/2.75	
5.90/2.75	6:	T:
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)         evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)         evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)      evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)         evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)      evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)         evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)         evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)         evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)    evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)         evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 0)         koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.75	
5.90/2.75		start location:	koat_start
5.90/2.75	
5.90/2.75		leaf cost:	0
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	A polynomial rank function with
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb3in) = V_4
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb1in) = V_4
5.90/2.75	
5.90/2.75		Pol(evalinsertsortbb2in) = V_4 + 1
5.90/2.75	
5.90/2.75	and size complexities
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 20
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))", 0-3) = 2*ar_1 + 10
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-0) = 2*ar_1 + 10
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-0) = 2*ar_1 + 4
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-2) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]", 0-3) = ?
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-0) = 1
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2
5.90/2.75	
5.90/2.75		S("evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3
5.90/2.75	
5.90/2.75	orients the transitions
5.90/2.75	
5.90/2.75		evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75		evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75		evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75	weakly and the transition
5.90/2.75	
5.90/2.75		evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75	strictly and produces the following problem:
5.90/2.75	
5.90/2.75	7:	T:
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)                     evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)                     evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)                  evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)                     evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)                  evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1^2 + 11*ar_1, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)                     evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75			(Comp: ?, Cost: 1)                     evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)                     evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.75	
5.90/2.75		start location:	koat_start
5.90/2.75	
5.90/2.75		leaf cost:	0
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Repeatedly propagating knowledge in problem 7 produces the following problem:
5.90/2.75	
5.90/2.75	8:	T:
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)                     evalinsertsortstart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 1)                     evalinsertsortentryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)                  evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3)) [ ar_1 >= ar_0 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)                     evalinsertsortbb5in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_1 ]
5.90/2.75	
5.90/2.75			(Comp: ar_1, Cost: 1)                  evalinsertsortbbin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, e, ar_0 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_3 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1^2 + 11*ar_1, Cost: 1)    evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 0 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1^2 + 11*ar_1, Cost: 1)    evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= ar_2 + 1 ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= e ]
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1^2 + 11*ar_1, Cost: 1)    evalinsertsortbb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb2in(ar_0, ar_1, ar_2, ar_3 - 1))
5.90/2.75	
5.90/2.75			(Comp: 2*ar_1, Cost: 1)                evalinsertsortbb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortbb5in(ar_0 + 1, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 2, Cost: 1)                     evalinsertsortreturnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstop(ar_0, ar_1, ar_2, ar_3))
5.90/2.75	
5.90/2.75			(Comp: 1, Cost: 0)                     koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalinsertsortstart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]
5.90/2.75	
5.90/2.75		start location:	koat_start
5.90/2.75	
5.90/2.75		leaf cost:	0
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Complexity upper bound 41*ar_1 + 6*ar_1^2 + 6
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Time: 0.139 sec (SMT: 0.117 sec)
5.90/2.75	
5.90/2.75	
5.90/2.75	----------------------------------------
5.90/2.75	
5.90/2.75	(2)
5.90/2.75	BOUNDS(1, n^2)
5.90/2.75	
5.90/2.75	----------------------------------------
5.90/2.75	
5.90/2.75	(3) Loat Proof (FINISHED)
5.90/2.75	
5.90/2.75	
5.90/2.75	### Pre-processing the ITS problem ###
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Initial linear ITS problem
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	      0: evalinsertsortstart -> evalinsertsortentryin : [], cost: 1
5.90/2.75	
5.90/2.75	      1: evalinsertsortentryin -> evalinsertsortbb5in : A'=1, [], cost: 1
5.90/2.75	
5.90/2.75	      2: evalinsertsortbb5in -> evalinsertsortbbin : [ B>=1+A ], cost: 1
5.90/2.75	
5.90/2.75	      3: evalinsertsortbb5in -> evalinsertsortreturnin : [ A>=B ], cost: 1
5.90/2.75	
5.90/2.75	      4: evalinsertsortbbin -> evalinsertsortbb2in : C'=free, D'=-1+A, [], cost: 1
5.90/2.75	
5.90/2.75	      5: evalinsertsortbb2in -> evalinsertsortbb4in : [ 0>=1+D ], cost: 1
5.90/2.75	
5.90/2.75	      6: evalinsertsortbb2in -> evalinsertsortbb3in : [ D>=0 ], cost: 1
5.90/2.75	
5.90/2.75	      7: evalinsertsortbb3in -> evalinsertsortbb1in : [ free_1>=1+C ], cost: 1
5.90/2.75	
5.90/2.75	      8: evalinsertsortbb3in -> evalinsertsortbb4in : [ C>=free_2 ], cost: 1
5.90/2.75	
5.90/2.75	      9: evalinsertsortbb1in -> evalinsertsortbb2in : D'=-1+D, [], cost: 1
5.90/2.75	
5.90/2.75	     10: evalinsertsortbb4in -> evalinsertsortbb5in : A'=1+A, [], cost: 1
5.90/2.75	
5.90/2.75	     11: evalinsertsortreturnin -> evalinsertsortstop : [], cost: 1
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Removed unreachable and leaf rules:
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	      0: evalinsertsortstart -> evalinsertsortentryin : [], cost: 1
5.90/2.75	
5.90/2.75	      1: evalinsertsortentryin -> evalinsertsortbb5in : A'=1, [], cost: 1
5.90/2.75	
5.90/2.75	      2: evalinsertsortbb5in -> evalinsertsortbbin : [ B>=1+A ], cost: 1
5.90/2.75	
5.90/2.75	      4: evalinsertsortbbin -> evalinsertsortbb2in : C'=free, D'=-1+A, [], cost: 1
5.90/2.75	
5.90/2.75	      5: evalinsertsortbb2in -> evalinsertsortbb4in : [ 0>=1+D ], cost: 1
5.90/2.75	
5.90/2.75	      6: evalinsertsortbb2in -> evalinsertsortbb3in : [ D>=0 ], cost: 1
5.90/2.75	
5.90/2.75	      7: evalinsertsortbb3in -> evalinsertsortbb1in : [ free_1>=1+C ], cost: 1
5.90/2.75	
5.90/2.75	      8: evalinsertsortbb3in -> evalinsertsortbb4in : [ C>=free_2 ], cost: 1
5.90/2.75	
5.90/2.75	      9: evalinsertsortbb1in -> evalinsertsortbb2in : D'=-1+D, [], cost: 1
5.90/2.75	
5.90/2.75	     10: evalinsertsortbb4in -> evalinsertsortbb5in : A'=1+A, [], cost: 1
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Simplified all rules, resulting in:
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	      0: evalinsertsortstart -> evalinsertsortentryin : [], cost: 1
5.90/2.75	
5.90/2.75	      1: evalinsertsortentryin -> evalinsertsortbb5in : A'=1, [], cost: 1
5.90/2.75	
5.90/2.75	      2: evalinsertsortbb5in -> evalinsertsortbbin : [ B>=1+A ], cost: 1
5.90/2.75	
5.90/2.75	      4: evalinsertsortbbin -> evalinsertsortbb2in : C'=free, D'=-1+A, [], cost: 1
5.90/2.75	
5.90/2.75	      5: evalinsertsortbb2in -> evalinsertsortbb4in : [ 0>=1+D ], cost: 1
5.90/2.75	
5.90/2.75	      6: evalinsertsortbb2in -> evalinsertsortbb3in : [ D>=0 ], cost: 1
5.90/2.75	
5.90/2.75	      7: evalinsertsortbb3in -> evalinsertsortbb1in : [], cost: 1
5.90/2.75	
5.90/2.75	      8: evalinsertsortbb3in -> evalinsertsortbb4in : [], cost: 1
5.90/2.75	
5.90/2.75	      9: evalinsertsortbb1in -> evalinsertsortbb2in : D'=-1+D, [], cost: 1
5.90/2.75	
5.90/2.75	     10: evalinsertsortbb4in -> evalinsertsortbb5in : A'=1+A, [], cost: 1
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	### Simplification by acceleration and chaining ###
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Eliminated locations (on linear paths):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     13: evalinsertsortbb5in -> evalinsertsortbb2in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2
5.90/2.75	
5.90/2.75	      5: evalinsertsortbb2in -> evalinsertsortbb4in : [ 0>=1+D ], cost: 1
5.90/2.75	
5.90/2.75	      6: evalinsertsortbb2in -> evalinsertsortbb3in : [ D>=0 ], cost: 1
5.90/2.75	
5.90/2.75	      8: evalinsertsortbb3in -> evalinsertsortbb4in : [], cost: 1
5.90/2.75	
5.90/2.75	     14: evalinsertsortbb3in -> evalinsertsortbb2in : D'=-1+D, [], cost: 2
5.90/2.75	
5.90/2.75	     10: evalinsertsortbb4in -> evalinsertsortbb5in : A'=1+A, [], cost: 1
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Eliminated locations (on tree-shaped paths):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     13: evalinsertsortbb5in -> evalinsertsortbb2in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2
5.90/2.75	
5.90/2.75	     16: evalinsertsortbb2in -> evalinsertsortbb2in : D'=-1+D, [ D>=0 ], cost: 3
5.90/2.75	
5.90/2.75	     17: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ 0>=1+D ], cost: 2
5.90/2.75	
5.90/2.75	     18: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ D>=0 ], cost: 3
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Accelerating simple loops of location 4.
5.90/2.75	
5.90/2.75	   Accelerating the following rules:
5.90/2.75	
5.90/2.75	     16: evalinsertsortbb2in -> evalinsertsortbb2in : D'=-1+D, [ D>=0 ], cost: 3
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	   Accelerated rule 16 with metering function 1+D, yielding the new rule 19.
5.90/2.75	
5.90/2.75	   Removing the simple loops: 16.
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Accelerated all simple loops using metering functions (where possible):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     13: evalinsertsortbb5in -> evalinsertsortbb2in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2
5.90/2.75	
5.90/2.75	     17: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ 0>=1+D ], cost: 2
5.90/2.75	
5.90/2.75	     18: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ D>=0 ], cost: 3
5.90/2.75	
5.90/2.75	     19: evalinsertsortbb2in -> evalinsertsortbb2in : D'=-1, [ D>=0 ], cost: 3+3*D
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Chained accelerated rules (with incoming rules):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     13: evalinsertsortbb5in -> evalinsertsortbb2in : C'=free, D'=-1+A, [ B>=1+A ], cost: 2
5.90/2.75	
5.90/2.75	     20: evalinsertsortbb5in -> evalinsertsortbb2in : C'=free, D'=-1, [ B>=1+A && -1+A>=0 ], cost: 2+3*A
5.90/2.75	
5.90/2.75	     17: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ 0>=1+D ], cost: 2
5.90/2.75	
5.90/2.75	     18: evalinsertsortbb2in -> evalinsertsortbb5in : A'=1+A, [ D>=0 ], cost: 3
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Eliminated locations (on tree-shaped paths):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     21: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1+A, [ B>=1+A && 0>=A ], cost: 4
5.90/2.75	
5.90/2.75	     22: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1+A, [ B>=1+A && -1+A>=0 ], cost: 5
5.90/2.75	
5.90/2.75	     23: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1, [ B>=1+A && -1+A>=0 ], cost: 4+3*A
5.90/2.75	
5.90/2.75	     24: evalinsertsortbb5in -> [11] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Accelerating simple loops of location 2.
5.90/2.75	
5.90/2.75	   Accelerating the following rules:
5.90/2.75	
5.90/2.75	     21: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1+A, [ B>=1+A && 0>=A ], cost: 4
5.90/2.75	
5.90/2.75	     22: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1+A, [ B>=1+A && -1+A>=0 ], cost: 5
5.90/2.75	
5.90/2.75	     23: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1+A, C'=free, D'=-1, [ B>=1+A && -1+A>=0 ], cost: 4+3*A
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	   Accelerated rule 21 with backward acceleration, yielding the new rule 25.
5.90/2.75	
5.90/2.75	   Accelerated rule 21 with backward acceleration, yielding the new rule 26.
5.90/2.75	
5.90/2.75	   Accelerated rule 22 with metering function -A+B, yielding the new rule 27.
5.90/2.75	
5.90/2.75	   Accelerated rule 23 with metering function -A+B, yielding the new rule 28.
5.90/2.75	
5.90/2.75	   Removing the simple loops: 21 22 23.
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Accelerated all simple loops using metering functions (where possible):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     24: evalinsertsortbb5in -> [11] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A
5.90/2.75	
5.90/2.75	     25: evalinsertsortbb5in -> evalinsertsortbb5in : A'=B, C'=free, D'=-2+B, [ B>=1+A && 0>=A && 0>=-1+B ], cost: -4*A+4*B
5.90/2.75	
5.90/2.75	     26: evalinsertsortbb5in -> evalinsertsortbb5in : A'=1, C'=free, D'=-1, [ B>=1+A && 0>=A && B>=1 ], cost: 4-4*A
5.90/2.75	
5.90/2.75	     27: evalinsertsortbb5in -> evalinsertsortbb5in : A'=B, C'=free, D'=-2+B, [ B>=1+A && -1+A>=0 ], cost: -5*A+5*B
5.90/2.75	
5.90/2.75	     28: evalinsertsortbb5in -> evalinsertsortbb5in : A'=B, C'=free, D'=-1, [ B>=1+A && -1+A>=0 ], cost: 3/2*(A-B)^2-5/2*A-3*A*(A-B)+5/2*B
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Chained accelerated rules (with incoming rules):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     12: evalinsertsortstart -> evalinsertsortbb5in : A'=1, [], cost: 2
5.90/2.75	
5.90/2.75	     29: evalinsertsortstart -> evalinsertsortbb5in : A'=B, C'=free, D'=-2+B, [ B>=2 ], cost: -3+5*B
5.90/2.75	
5.90/2.75	     30: evalinsertsortstart -> evalinsertsortbb5in : A'=B, C'=free, D'=-1, [ B>=2 ], cost: -7/2+3/2*(-1+B)^2+11/2*B
5.90/2.75	
5.90/2.75	     24: evalinsertsortbb5in -> [11] : [ B>=1+A && -1+A>=0 ], cost: 2+3*A
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Eliminated locations (on tree-shaped paths):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     31: evalinsertsortstart -> [11] : A'=1, [ B>=2 ], cost: 7
5.90/2.75	
5.90/2.75	     32: evalinsertsortstart -> [13] : [ B>=2 ], cost: -3+5*B
5.90/2.75	
5.90/2.75	     33: evalinsertsortstart -> [13] : [ B>=2 ], cost: -7/2+3/2*(-1+B)^2+11/2*B
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Applied pruning (of leafs and parallel rules):
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     32: evalinsertsortstart -> [13] : [ B>=2 ], cost: -3+5*B
5.90/2.75	
5.90/2.75	     33: evalinsertsortstart -> [13] : [ B>=2 ], cost: -7/2+3/2*(-1+B)^2+11/2*B
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	### Computing asymptotic complexity ###
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Fully simplified ITS problem
5.90/2.75	
5.90/2.75	   Start location: evalinsertsortstart
5.90/2.75	
5.90/2.75	     32: evalinsertsortstart -> [13] : [ B>=2 ], cost: -3+5*B
5.90/2.75	
5.90/2.75	     33: evalinsertsortstart -> [13] : [ B>=2 ], cost: -7/2+3/2*(-1+B)^2+11/2*B
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Computing asymptotic complexity for rule 32
5.90/2.75	
5.90/2.75	   Solved the limit problem by the following transformations:
5.90/2.75	
5.90/2.75	      Created initial limit problem:
5.90/2.75	
5.90/2.75	      -1+B (+/+!), -3+5*B (+) [not solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	      removing all constraints (solved by SMT)
5.90/2.75	
5.90/2.75	      resulting limit problem: [solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	      applying transformation rule (C) using substitution {B==n}
5.90/2.75	
5.90/2.75	      resulting limit problem:
5.90/2.75	
5.90/2.75	      [solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	   Solution:
5.90/2.75	
5.90/2.75	      B / n
5.90/2.75	
5.90/2.75	   Resulting cost -3+5*n has complexity: Poly(n^1)
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Found new complexity Poly(n^1).
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Computing asymptotic complexity for rule 33
5.90/2.75	
5.90/2.75	   Solved the limit problem by the following transformations:
5.90/2.75	
5.90/2.75	      Created initial limit problem:
5.90/2.75	
5.90/2.75	      -1+B (+/+!), -2+3/2*B^2+5/2*B (+) [not solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	      removing all constraints (solved by SMT)
5.90/2.75	
5.90/2.75	      resulting limit problem: [solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	      applying transformation rule (C) using substitution {B==n}
5.90/2.75	
5.90/2.75	      resulting limit problem:
5.90/2.75	
5.90/2.75	      [solved]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	   Solution:
5.90/2.75	
5.90/2.75	      B / n
5.90/2.75	
5.90/2.75	   Resulting cost -2+5/2*n+3/2*n^2 has complexity: Poly(n^2)
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Found new complexity Poly(n^2).
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	Obtained the following overall complexity (w.r.t. the length of the input n):
5.90/2.75	
5.90/2.75	   Complexity:  Poly(n^2)
5.90/2.75	
5.90/2.75	   Cpx degree:  2
5.90/2.75	
5.90/2.75	   Solved cost: -2+5/2*n+3/2*n^2
5.90/2.75	
5.90/2.75	   Rule cost:   -7/2+3/2*(-1+B)^2+11/2*B
5.90/2.75	
5.90/2.75	   Rule guard:  [ B>=2 ]
5.90/2.75	
5.90/2.75	
5.90/2.75	
5.90/2.75	WORST_CASE(Omega(n^2),?)
5.90/2.75	
5.90/2.75	
5.90/2.75	----------------------------------------
5.90/2.75	
5.90/2.75	(4)
5.90/2.75	BOUNDS(n^2, INF)
5.97/2.77	EOF