/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.koat
# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1).

(0) CpxIntTrs
(1) Koat Proof [FINISHED, 431 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 1458 ms]
(4) BOUNDS(n^1, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalcomplexstart(A, B, C, D, E) -> Com_1(evalcomplexentryin(A, B, C, D, E)) :|: TRUE
evalcomplexentryin(A, B, C, D, E) -> Com_1(evalcomplexbb10in(B, A, C, D, E)) :|: TRUE
evalcomplexbb10in(A, B, C, D, E) -> Com_1(evalcomplexbb8in(A, B, A, B, E)) :|: 29 >= B
evalcomplexbb10in(A, B, C, D, E) -> Com_1(evalcomplexreturnin(A, B, C, D, E)) :|: B >= 30
evalcomplexbb8in(A, B, C, D, E) -> Com_1(evalcomplexbb1in(A, B, C, D, E)) :|: D >= C + 1
evalcomplexbb8in(A, B, C, D, E) -> Com_1(evalcomplexbb9in(A, B, C, D, E)) :|: C >= D
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb7in(A, B, C, D, C + 7)) :|: C >= 6 && 2 >= C
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb7in(A, B, C, D, C + 7)) :|: C >= 6
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb6in(A, B, C, D, C + 7)) :|: C >= 6 && C >= 3 && 5 >= C
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb7in(A, B, C, D, C + 2)) :|: 5 >= C && 7 >= C
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb7in(A, B, C, D, C + 2)) :|: 5 >= C && C >= 11
evalcomplexbb1in(A, B, C, D, E) -> Com_1(evalcomplexbb6in(A, B, C, D, C + 2)) :|: 5 >= C && C >= 8 && 10 >= C
evalcomplexbb7in(A, B, C, D, E) -> Com_1(evalcomplexbb8in(A, B, E, D + 1, E)) :|: TRUE
evalcomplexbb6in(A, B, C, D, E) -> Com_1(evalcomplexbb8in(A, B, E, D + 10, E)) :|: TRUE
evalcomplexbb9in(A, B, C, D, E) -> Com_1(evalcomplexbb10in(C - 10, D + 2, C, D, E)) :|: TRUE
evalcomplexreturnin(A, B, C, D, E) -> Com_1(evalcomplexstop(A, B, C, D, E)) :|: TRUE

The start-symbols are:[evalcomplexstart_5]


----------------------------------------

(1) Koat Proof (FINISHED)
YES(?, 65*ar_0 + 12*ar_1 + 2304)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 /\ 2 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 /\ ar_2 >= 3 /\ 5 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ ar_2 >= 11 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ ar_2 >= 8 /\ 10 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 10, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Testing for reachability in the complexity graph removes the following transitions from problem 1:

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 /\ 2 >= ar_2 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 /\ ar_2 >= 3 /\ 5 >= ar_2 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ ar_2 >= 11 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ ar_2 >= 8 /\ 10 >= ar_2 ]

	evalcomplexbb6in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 10, ar_4))

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: ?, Cost: 1)    evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: ?, Cost: 1)    evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 2 produces the following problem:

3:	T:

		(Comp: ?, Cost: 1)    evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: ?, Cost: 1)    evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)    evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalcomplexbb7in) = 2

	Pol(evalcomplexbb8in) = 2

	Pol(evalcomplexbb9in) = 2

	Pol(evalcomplexbb10in) = 2

	Pol(evalcomplexbb1in) = 2

	Pol(evalcomplexreturnin) = 1

	Pol(evalcomplexstop) = 0

	Pol(evalcomplexentryin) = 2

	Pol(evalcomplexstart) = 2

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

	evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

strictly and produces the following problem:

4:	T:

		(Comp: ?, Cost: 1)    evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: 2, Cost: 1)    evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: 2, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ?, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 1, Cost: 1)    evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)    evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalcomplexbb7in) = -V_4 + 27

	Pol(evalcomplexbb8in) = -V_4 + 28

	Pol(evalcomplexbb9in) = -V_4 + 28

	Pol(evalcomplexbb10in) = -V_2 + 30

	Pol(evalcomplexbb1in) = -V_4 + 27

	Pol(evalcomplexreturnin) = -V_2

	Pol(evalcomplexstop) = -V_2

	Pol(evalcomplexentryin) = -V_1 + 30

	Pol(evalcomplexstart) = -V_1 + 30

	Pol(koat_start) = -V_1 + 30

orients all transitions weakly and the transition

	evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

strictly and produces the following problem:

5:	T:

		(Comp: ?, Cost: 1)            evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: ?, Cost: 1)            evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)            evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)            evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: 2, Cost: 1)            evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)            evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)            evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: 2, Cost: 1)            evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ar_0 + 30, Cost: 1)    evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 1, Cost: 1)            evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)            evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)            koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalcomplexbb9in) = 1

	Pol(evalcomplexbb10in) = 0

	Pol(evalcomplexbb8in) = 2

	Pol(evalcomplexbb1in) = 2

	Pol(evalcomplexbb7in) = 2

and size complexities

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-0) = ar_0

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-1) = ar_1

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-2) = ar_2

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-3) = ar_3

	S("koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]", 0-4) = ar_4

	S("evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ar_0

	S("evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ar_1

	S("evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ar_2

	S("evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ar_3

	S("evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ar_4

	S("evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))", 0-0) = ar_1

	S("evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))", 0-1) = ar_0

	S("evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))", 0-2) = ar_2

	S("evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))", 0-3) = ar_3

	S("evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))", 0-4) = ar_4

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]", 0-0) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]", 0-1) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]", 0-2) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]", 0-3) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]", 0-4) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]", 0-0) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]", 0-1) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]", 0-2) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]", 0-3) = ?

	S("evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]", 0-4) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]", 0-0) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]", 0-1) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]", 0-2) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]", 0-3) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]", 0-4) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]", 0-0) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]", 0-1) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]", 0-2) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]", 0-3) = ?

	S("evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]", 0-4) = ?

	S("evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-0) = ?

	S("evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-1) = ?

	S("evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-2) = ?

	S("evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-3) = ?

	S("evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))", 0-4) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]", 0-0) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]", 0-1) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]", 0-2) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]", 0-3) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]", 0-4) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\\ 7 >= ar_2 ]", 0-0) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\\ 7 >= ar_2 ]", 0-1) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\\ 7 >= ar_2 ]", 0-2) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\\ 7 >= ar_2 ]", 0-3) = ?

	S("evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\\ 7 >= ar_2 ]", 0-4) = ?

	S("evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))", 0-0) = ?

	S("evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))", 0-1) = ?

	S("evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))", 0-2) = ?

	S("evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))", 0-3) = ?

	S("evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))", 0-4) = ?

	S("evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))", 0-0) = ?

	S("evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))", 0-1) = ?

	S("evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))", 0-2) = ?

	S("evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))", 0-3) = ?

	S("evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))", 0-4) = ?

orients the transitions

	evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

	evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

	evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

	evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

weakly and the transitions

	evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

	evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

strictly and produces the following problem:

6:	T:

		(Comp: ?, Cost: 1)              evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4))

		(Comp: 2*ar_0 + 60, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4))

		(Comp: ?, Cost: 1)              evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: ?, Cost: 1)              evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ ar_2 >= 6 ]

		(Comp: 2, Cost: 1)              evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 2*ar_0 + 60, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_3 ]

		(Comp: ?, Cost: 1)              evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_3 >= ar_2 + 1 ]

		(Comp: 2, Cost: 1)              evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ar_0 + 30, Cost: 1)      evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 1, Cost: 1)              evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)              evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 6 to obtain the following invariants:

  For symbol evalcomplexbb1in: -X_3 + X_4 - 1 >= 0 /\ -X_2 + X_4 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_2 + 29 >= 0

  For symbol evalcomplexbb7in: X_4 - X_5 + 6 >= 0 /\ X_3 - X_5 + 7 >= 0 /\ -X_3 + X_5 - 2 >= 0 /\ -X_1 + X_5 - 2 >= 0 /\ -X_3 + X_4 - 1 >= 0 /\ -X_2 + X_4 >= 0 /\ -X_1 + X_4 - 1 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_2 + 29 >= 0

  For symbol evalcomplexbb8in: -X_2 + X_4 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_2 + 29 >= 0

  For symbol evalcomplexbb9in: X_3 - X_4 >= 0 /\ -X_2 + X_4 >= 0 /\ -X_2 + X_3 >= 0 /\ -X_1 + X_3 >= 0 /\ -X_2 + 29 >= 0

  For symbol evalcomplexreturnin: X_2 - 30 >= 0





This yielded the following problem:

7:	T:

		(Comp: 1, Cost: 0)              koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)              evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)              evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: ar_0 + 30, Cost: 1)      evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 2, Cost: 1)              evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: ?, Cost: 1)              evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_3 >= ar_2 + 1 ]

		(Comp: 2*ar_0 + 60, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_2 >= ar_3 ]

		(Comp: 2, Cost: 1)              evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 - 30 >= 0 ]

		(Comp: ?, Cost: 1)              evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_2 >= 6 ]

		(Comp: ?, Cost: 1)              evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: 2*ar_0 + 60, Cost: 1)    evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_1 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 ]

		(Comp: ?, Cost: 1)              evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4)) [ ar_3 - ar_4 + 6 >= 0 /\ ar_2 - ar_4 + 7 >= 0 /\ -ar_2 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = -15*V_1 - 3*V_2 + 537

	Pol(evalcomplexstart) = -15*V_1 - 3*V_2 + 537

	Pol(evalcomplexentryin) = -15*V_1 - 3*V_2 + 537

	Pol(evalcomplexbb10in) = -3*V_1 - 15*V_2 + 537

	Pol(evalcomplexbb8in) = -18*V_2 - 3*V_3 + 3*V_4 + 537

	Pol(evalcomplexreturnin) = -3*V_1 - 15*V_2 + 537

	Pol(evalcomplexbb1in) = -18*V_2 - 3*V_3 + 3*V_4 + 536

	Pol(evalcomplexbb9in) = -3*V_3 - 15*V_4 + 537

	Pol(evalcomplexstop) = -3*V_1 - 15*V_2 + 537

	Pol(evalcomplexbb7in) = -18*V_2 - 3*V_3 + 3*V_4 + 535

orients all transitions weakly and the transitions

	evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_3 >= ar_2 + 1 ]

	evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4)) [ ar_3 - ar_4 + 6 >= 0 /\ ar_2 - ar_4 + 7 >= 0 /\ -ar_2 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_2 >= 6 ]

	evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ 5 >= ar_2 /\ 7 >= ar_2 ]

strictly and produces the following problem:

8:	T:

		(Comp: 1, Cost: 0)                         koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)                         evalcomplexstart(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4))

		(Comp: 1, Cost: 1)                         evalcomplexentryin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_1, ar_0, ar_2, ar_3, ar_4))

		(Comp: ar_0 + 30, Cost: 1)                 evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_0, ar_1, ar_4)) [ 29 >= ar_1 ]

		(Comp: 2, Cost: 1)                         evalcomplexbb10in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 >= 30 ]

		(Comp: 15*ar_0 + 3*ar_1 + 537, Cost: 1)    evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_3 >= ar_2 + 1 ]

		(Comp: 2*ar_0 + 60, Cost: 1)               evalcomplexbb8in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_2 >= ar_3 ]

		(Comp: 2, Cost: 1)                         evalcomplexreturnin(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexstop(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_1 - 30 >= 0 ]

		(Comp: 15*ar_0 + 3*ar_1 + 537, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 7)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ ar_2 >= 6 ]

		(Comp: 15*ar_0 + 3*ar_1 + 537, Cost: 1)    evalcomplexbb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_2 + 2)) [ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 /\ 5 >= ar_2 /\ 7 >= ar_2 ]

		(Comp: 2*ar_0 + 60, Cost: 1)               evalcomplexbb9in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb10in(ar_2 - 10, ar_3 + 2, ar_2, ar_3, ar_4)) [ ar_2 - ar_3 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_1 + ar_2 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 ]

		(Comp: 15*ar_0 + 3*ar_1 + 537, Cost: 1)    evalcomplexbb7in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalcomplexbb8in(ar_0, ar_1, ar_4, ar_3 + 1, ar_4)) [ ar_3 - ar_4 + 6 >= 0 /\ ar_2 - ar_4 + 7 >= 0 /\ -ar_2 + ar_4 - 2 >= 0 /\ -ar_0 + ar_4 - 2 >= 0 /\ -ar_2 + ar_3 - 1 >= 0 /\ -ar_1 + ar_3 >= 0 /\ -ar_0 + ar_3 - 1 >= 0 /\ -ar_0 + ar_2 >= 0 /\ -ar_1 + 29 >= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 65*ar_0 + 12*ar_1 + 2304



Time: 0.405 sec (SMT: 0.321 sec)


----------------------------------------

(2)
BOUNDS(1, n^1)

----------------------------------------

(3) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalcomplexstart

      0: evalcomplexstart -> evalcomplexentryin : [], cost: 1

      1: evalcomplexentryin -> evalcomplexbb10in : A'=B, B'=A, [], cost: 1

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      3: evalcomplexbb10in -> evalcomplexreturnin : [ B>=30 ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

      5: evalcomplexbb8in -> evalcomplexbb9in : [ C>=D ], cost: 1

      6: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 && 2>=C ], cost: 1

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      8: evalcomplexbb1in -> evalcomplexbb6in : E'=7+C, [ C>=6 && C>=3 && 5>=C ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C && 7>=C ], cost: 1

     10: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C && C>=11 ], cost: 1

     11: evalcomplexbb1in -> evalcomplexbb6in : E'=2+C, [ 5>=C && C>=8 && 10>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1

     13: evalcomplexbb6in -> evalcomplexbb8in : C'=E, D'=10+D, [], cost: 1

     14: evalcomplexbb9in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [], cost: 1

     15: evalcomplexreturnin -> evalcomplexstop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalcomplexstart

      0: evalcomplexstart -> evalcomplexentryin : [], cost: 1

      1: evalcomplexentryin -> evalcomplexbb10in : A'=B, B'=A, [], cost: 1

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

      5: evalcomplexbb8in -> evalcomplexbb9in : [ C>=D ], cost: 1

      6: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 && 2>=C ], cost: 1

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      8: evalcomplexbb1in -> evalcomplexbb6in : E'=7+C, [ C>=6 && C>=3 && 5>=C ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C && 7>=C ], cost: 1

     10: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C && C>=11 ], cost: 1

     11: evalcomplexbb1in -> evalcomplexbb6in : E'=2+C, [ 5>=C && C>=8 && 10>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1

     13: evalcomplexbb6in -> evalcomplexbb8in : C'=E, D'=10+D, [], cost: 1

     14: evalcomplexbb9in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [], cost: 1



Removed rules with unsatisfiable guard:

   Start location: evalcomplexstart

      0: evalcomplexstart -> evalcomplexentryin : [], cost: 1

      1: evalcomplexentryin -> evalcomplexbb10in : A'=B, B'=A, [], cost: 1

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

      5: evalcomplexbb8in -> evalcomplexbb9in : [ C>=D ], cost: 1

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C && 7>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1

     13: evalcomplexbb6in -> evalcomplexbb8in : C'=E, D'=10+D, [], cost: 1

     14: evalcomplexbb9in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [], cost: 1



Simplified all rules, resulting in:

   Start location: evalcomplexstart

      0: evalcomplexstart -> evalcomplexentryin : [], cost: 1

      1: evalcomplexentryin -> evalcomplexbb10in : A'=B, B'=A, [], cost: 1

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

      5: evalcomplexbb8in -> evalcomplexbb9in : [ C>=D ], cost: 1

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1

     13: evalcomplexbb6in -> evalcomplexbb8in : C'=E, D'=10+D, [], cost: 1

     14: evalcomplexbb9in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [], cost: 1



### Simplification by acceleration and chaining ###



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalcomplexstart

      0: evalcomplexstart -> evalcomplexentryin : [], cost: 1

      1: evalcomplexentryin -> evalcomplexbb10in : A'=B, B'=A, [], cost: 1

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

      5: evalcomplexbb8in -> evalcomplexbb9in : [ C>=D ], cost: 1

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1

     14: evalcomplexbb9in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [], cost: 1



Eliminated locations (on linear paths):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

      4: evalcomplexbb8in -> evalcomplexbb1in : [ D>=1+C ], cost: 1

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2

      7: evalcomplexbb1in -> evalcomplexbb7in : E'=7+C, [ C>=6 ], cost: 1

      9: evalcomplexbb1in -> evalcomplexbb7in : E'=2+C, [ 5>=C ], cost: 1

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2

     18: evalcomplexbb8in -> evalcomplexbb7in : E'=7+C, [ D>=1+C && C>=6 ], cost: 2

     19: evalcomplexbb8in -> evalcomplexbb7in : E'=2+C, [ D>=1+C && 5>=C ], cost: 2

     12: evalcomplexbb7in -> evalcomplexbb8in : C'=E, D'=1+D, [], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2

     20: evalcomplexbb8in -> evalcomplexbb8in : C'=7+C, D'=1+D, E'=7+C, [ D>=1+C && C>=6 ], cost: 3

     21: evalcomplexbb8in -> evalcomplexbb8in : C'=2+C, D'=1+D, E'=2+C, [ D>=1+C && 5>=C ], cost: 3



Accelerating simple loops of location 3.

   Accelerating the following rules:

     20: evalcomplexbb8in -> evalcomplexbb8in : C'=7+C, D'=1+D, E'=7+C, [ D>=1+C && C>=6 ], cost: 3

     21: evalcomplexbb8in -> evalcomplexbb8in : C'=2+C, D'=1+D, E'=2+C, [ D>=1+C && 5>=C ], cost: 3



   Accelerated rule 20 with metering function meter (where 6*meter==-C+D), yielding the new rule 22.

   Accelerated rule 21 with NONTERM (after adding C>=D), yielding the new rule 23.

   Accelerated rule 21 with backward acceleration, yielding the new rule 24.

      During metering: Instantiating temporary variables by {k==1}

   Removing the simple loops: 20 21.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2

     22: evalcomplexbb8in -> evalcomplexbb8in : C'=C+7*meter, D'=D+meter, E'=C+7*meter, [ D>=1+C && C>=6 && 6*meter==-C+D && meter>=1 ], cost: 3*meter

     23: evalcomplexbb8in -> [10] : [ D>=1+C && 5>=C && C>=D ], cost: INF

     24: evalcomplexbb8in -> evalcomplexbb8in : C'=2*k+C, D'=k+D, E'=2*k+C, [ D>=1+C && 5>=C && k>0 && -1+k+D>=-1+2*k+C && 5>=-2+2*k+C ], cost: 3*k



Chained accelerated rules (with incoming rules):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

     25: evalcomplexbb10in -> evalcomplexbb8in : C'=A+7*meter, D'=meter+B, E'=A+7*meter, [ 29>=B && B>=1+A && A>=6 && 6*meter==-A+B && meter>=1 ], cost: 1+3*meter

     26: evalcomplexbb10in -> evalcomplexbb8in : C'=2*k+A, D'=k+B, E'=2*k+A, [ 29>=B && B>=1+A && 5>=A && k>0 && -1+k+B>=-1+2*k+A && 5>=-2+2*k+A ], cost: 1+3*k

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

      2: evalcomplexbb10in -> evalcomplexbb8in : C'=A, D'=B, [ 29>=B ], cost: 1

     25: evalcomplexbb10in -> evalcomplexbb8in : C'=A+7*meter, D'=meter+B, E'=A+7*meter, [ 29>=B && B>=1+A && A>=6 && 6*meter==-A+B && meter>=1 ], cost: 1+3*meter

     26: evalcomplexbb10in -> evalcomplexbb8in : C'=2*k+A, D'=k+B, E'=2*k+A, [ 29>=B && B>=1+A && 5>=A && k>0 && -1+k+B>=-1+2*k+A && 5>=-2+2*k+A ], cost: 1+3*k

     17: evalcomplexbb8in -> evalcomplexbb10in : A'=-10+C, B'=2+D, [ C>=D ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

     27: evalcomplexbb10in -> evalcomplexbb10in : A'=-10+A, B'=2+B, C'=A, D'=B, [ 29>=B && A>=B ], cost: 3

     28: evalcomplexbb10in -> evalcomplexbb10in : A'=-10+A+7*meter, B'=2+meter+B, C'=A+7*meter, D'=meter+B, E'=A+7*meter, [ 29>=B && B>=1+A && A>=6 && 6*meter==-A+B && meter>=1 ], cost: 3+3*meter

     29: evalcomplexbb10in -> evalcomplexbb10in : A'=-10+2*k+A, B'=2+k+B, C'=2*k+A, D'=k+B, E'=2*k+A, [ 29>=B && B>=1+A && 5>=A && k>0 && -1+k+B>=-1+2*k+A && 5>=-2+2*k+A && 2*k+A>=k+B ], cost: 3+3*k



Accelerating simple loops of location 2.

   Simplified some of the simple loops (and removed duplicate rules).

   Accelerating the following rules:

     27: evalcomplexbb10in -> evalcomplexbb10in : A'=-10+A, B'=2+B, C'=A, D'=B, [ 29>=B && A>=B ], cost: 3

     28: evalcomplexbb10in -> evalcomplexbb10in : A'=-10+A+7*meter, B'=2+meter+B, C'=A+7*meter, D'=meter+B, E'=A+7*meter, [ 29>=B && B>=1+A && A>=6 && 6*meter==-A+B && meter>=1 ], cost: 3+3*meter

     29: evalcomplexbb10in -> evalcomplexbb10in : A'=-10-A+2*B, B'=2-A+2*B, C'=-A+2*B, D'=-A+2*B, E'=-A+2*B, [ 29>=B && B>=1+A && 5>=A && 5>=-2-A+2*B ], cost: 3-3*A+3*B



   Accelerated rule 27 with metering function meter_1 (where 12*meter_1==A-B) (after adding A<=B), yielding the new rule 30.

   Accelerated rule 27 with backward acceleration, yielding the new rule 31.

      During metering: Instantiating temporary variables by {meter==1}

   Accelerated rule 28 with metering function meter_2 (where 6*meter_2==6+A-B), yielding the new rule 32.

   Found no metering function for rule 29 (rule is too complicated).

      During metering: Instantiating temporary variables by {k_1==1,meter==1}

   Removing the simple loops: 27 28.



Accelerated all simple loops using metering functions (where possible):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

     29: evalcomplexbb10in -> evalcomplexbb10in : A'=-10-A+2*B, B'=2-A+2*B, C'=-A+2*B, D'=-A+2*B, E'=-A+2*B, [ 29>=B && B>=1+A && 5>=A && 5>=-2-A+2*B ], cost: 3-3*A+3*B

     30: evalcomplexbb10in -> evalcomplexbb10in : A'=A-10*meter_1, B'=2*meter_1+B, C'=10+A-10*meter_1, D'=-2+2*meter_1+B, [ 29>=B && A>=B && A<=B && 12*meter_1==A-B && meter_1>=1 ], cost: 3*meter_1

     31: evalcomplexbb10in -> evalcomplexbb10in : A'=-10*k_1+A, B'=2*k_1+B, C'=10-10*k_1+A, D'=-2+2*k_1+B, [ 29>=B && A>=B && k_1>0 && 29>=-2+2*k_1+B && 10-10*k_1+A>=-2+2*k_1+B ], cost: 3*k_1

     32: evalcomplexbb10in -> evalcomplexbb10in : A'=A-3*meter_2, B'=3*meter_2+B, C'=10+A-3*meter_2, D'=-2+3*meter_2+B, E'=10+A-3*meter_2, [ 29>=B && A>=6 && 6==-A+B && 6*meter_2==6+A-B && meter_2>=1 ], cost: 6*meter_2



Chained accelerated rules (with incoming rules):

   Start location: evalcomplexstart

     16: evalcomplexstart -> evalcomplexbb10in : A'=B, B'=A, [], cost: 2

     33: evalcomplexstart -> evalcomplexbb10in : A'=-10+2*A-B, B'=2+2*A-B, C'=2*A-B, D'=2*A-B, E'=2*A-B, [ 29>=A && A>=1+B && 5>=B && 5>=-2+2*A-B ], cost: 5+3*A-3*B

     34: evalcomplexstart -> evalcomplexbb10in : A'=-10*k_1+B, B'=2*k_1+A, C'=10-10*k_1+B, D'=-2+2*k_1+A, [ 29>=A && B>=A && k_1>0 && 29>=-2+2*k_1+A && 10-10*k_1+B>=-2+2*k_1+A ], cost: 2+3*k_1



Removed unreachable locations (and leaf rules with constant cost):

   Start location: evalcomplexstart

     33: evalcomplexstart -> evalcomplexbb10in : A'=-10+2*A-B, B'=2+2*A-B, C'=2*A-B, D'=2*A-B, E'=2*A-B, [ 29>=A && A>=1+B && 5>=B && 5>=-2+2*A-B ], cost: 5+3*A-3*B

     34: evalcomplexstart -> evalcomplexbb10in : A'=-10*k_1+B, B'=2*k_1+A, C'=10-10*k_1+B, D'=-2+2*k_1+A, [ 29>=A && B>=A && k_1>0 && 29>=-2+2*k_1+A && 10-10*k_1+B>=-2+2*k_1+A ], cost: 2+3*k_1



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalcomplexstart

     33: evalcomplexstart -> evalcomplexbb10in : A'=-10+2*A-B, B'=2+2*A-B, C'=2*A-B, D'=2*A-B, E'=2*A-B, [ 29>=A && A>=1+B && 5>=B && 5>=-2+2*A-B ], cost: 5+3*A-3*B

     34: evalcomplexstart -> evalcomplexbb10in : A'=-10*k_1+B, B'=2*k_1+A, C'=10-10*k_1+B, D'=-2+2*k_1+A, [ 29>=A && B>=A && k_1>0 && 29>=-2+2*k_1+A && 10-10*k_1+B>=-2+2*k_1+A ], cost: 2+3*k_1



Computing asymptotic complexity for rule 33

   Simplified the guard:

     33: evalcomplexstart -> evalcomplexbb10in : A'=-10+2*A-B, B'=2+2*A-B, C'=2*A-B, D'=2*A-B, E'=2*A-B, [ A>=1+B && 5>=B && 5>=-2+2*A-B ], cost: 5+3*A-3*B

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      6-B (+/+!), 5+3*A-3*B (+), 8-2*A+B (+/+!), A-B (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==-n,B==-2*n}

      resulting limit problem:

      [solved]



   Solution:

      A / -n

      B / -2*n

   Resulting cost 5+3*n has complexity: Poly(n^1)



Found new complexity Poly(n^1).



Computing asymptotic complexity for rule 34

   Simplified the guard:

     34: evalcomplexstart -> evalcomplexbb10in : A'=-10*k_1+B, B'=2*k_1+A, C'=10-10*k_1+B, D'=-2+2*k_1+A, [ k_1>0 && 29>=-2+2*k_1+A && 10-10*k_1+B>=-2+2*k_1+A ], cost: 2+3*k_1

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      32-2*k_1-A (+/+!), k_1 (+/+!), 13-12*k_1-A+B (+/+!), 2+3*k_1 (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {k_1==n,A==-2*n,B==10*n}

      resulting limit problem:

      [solved]



   Solution:

      k_1 / n

      A / -2*n

      B / 10*n

   Resulting cost 2+3*n has complexity: Poly(n^1)



Obtained the following overall complexity (w.r.t. the length of the input n):

   Complexity:  Poly(n^1)

   Cpx degree:  1

   Solved cost: 5+3*n

   Rule cost:   5+3*A-3*B

   Rule guard:  [ A>=1+B && 5>=B && 5>=-2+2*A-B ]



WORST_CASE(Omega(n^1),?)


----------------------------------------

(4)
BOUNDS(n^1, INF)