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


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WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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, 392 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 829 ms]
(4) BOUNDS(n^1, INF)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalEx4start(A, B, C, D) -> Com_1(evalEx4entryin(A, B, C, D)) :|: TRUE
evalEx4entryin(A, B, C, D) -> Com_1(evalEx4bb4in(1, A, C, D)) :|: TRUE
evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4bb2in(A, B, 0, B)) :|: A >= 1 && A <= 1
evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4returnin(A, B, C, D)) :|: 0 >= A
evalEx4bb4in(A, B, C, D) -> Com_1(evalEx4returnin(A, B, C, D)) :|: A >= 2
evalEx4bb2in(A, B, C, D) -> Com_1(evalEx4bb4in(C, D, C, D)) :|: 0 >= D
evalEx4bb2in(A, B, C, D) -> Com_1(evalEx4bb3in(A, B, C, D)) :|: D >= 1
evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb1in(A, B, C, D)) :|: 0 >= E + 1
evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb1in(A, B, C, D)) :|: E >= 1
evalEx4bb3in(A, B, C, D) -> Com_1(evalEx4bb4in(C, D, C, D)) :|: TRUE
evalEx4bb1in(A, B, C, D) -> Com_1(evalEx4bb2in(A, B, 1, D - 1)) :|: TRUE
evalEx4returnin(A, B, C, D) -> Com_1(evalEx4stop(A, B, C, D)) :|: TRUE

The start-symbols are:[evalEx4start_4]


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(1) Koat Proof (FINISHED)
YES(?, 75*ar_0 + 42)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))

		(Comp: ?, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 1 produces the following problem:

2:	T:

		(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

		(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))

		(Comp: ?, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalEx4start) = 2

	Pol(evalEx4entryin) = 2

	Pol(evalEx4bb4in) = 2

	Pol(evalEx4bb2in) = 2

	Pol(evalEx4returnin) = 1

	Pol(evalEx4bb3in) = 2

	Pol(evalEx4bb1in) = 2

	Pol(evalEx4stop) = 0

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

	evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

	evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

		(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ 0 >= ar_3 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_3 >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ 0 >= e + 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ e >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1))

		(Comp: 2, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Applied AI with 'oct' on problem 3 to obtain the following invariants:

  For symbol evalEx4bb1in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0

  For symbol evalEx4bb2in: X_2 - X_4 >= 0 /\ X_3 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0

  For symbol evalEx4bb3in: X_2 - X_4 >= 0 /\ X_4 - 1 >= 0 /\ X_3 + X_4 - 1 >= 0 /\ X_2 + X_4 - 2 >= 0 /\ X_1 + X_4 - 2 >= 0 /\ -X_1 + X_4 >= 0 /\ X_3 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ -X_1 + X_3 + 1 >= 0 /\ X_2 - 1 >= 0 /\ X_1 + X_2 - 2 >= 0 /\ -X_1 + X_2 >= 0 /\ -X_1 + 1 >= 0 /\ X_1 - 1 >= 0





This yielded the following problem:

4:	T:

		(Comp: 1, Cost: 0)    koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)    evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: ?, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]

		(Comp: ?, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]

		(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: 2, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: ?, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: 1, Cost: 1)    evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: 1, Cost: 1)    evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = 5*V_1 + 2

	Pol(evalEx4start) = 5*V_1 + 2

	Pol(evalEx4returnin) = 2*V_1 + 5*V_2

	Pol(evalEx4stop) = 2*V_1 + 5*V_2

	Pol(evalEx4bb1in) = 5*V_4

	Pol(evalEx4bb2in) = 2*V_1 + 2*V_3 + 5*V_4

	Pol(evalEx4bb3in) = 2*V_3 + 5*V_4 + 1

	Pol(evalEx4bb4in) = 2*V_1 + 5*V_2

	Pol(evalEx4entryin) = 5*V_1 + 2

orients all transitions weakly and the transitions

	evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

	evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]

	evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]

	evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]

	evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

strictly and produces the following problem:

5:	T:

		(Comp: 1, Cost: 0)             koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)             evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]

		(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]

		(Comp: 5*ar_0 + 2, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]

		(Comp: ?, Cost: 1)             evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]

		(Comp: 2, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: 2, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: ?, Cost: 1)             evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: 1, Cost: 1)             evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: 1, Cost: 1)             evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalEx4bb4in) = 2*V_1

	Pol(evalEx4bb2in) = 2*V_3 + 1

and size complexities

	S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-0) = ar_0

	S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_1

	S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-2) = ar_2

	S("evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_3

	S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-0) = 1

	S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-1) = ar_0

	S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-2) = ar_2

	S("evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))", 0-3) = ar_3

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-0) = 1

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-1) = ar_0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-2) = 0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]", 0-3) = ar_0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-0) = 1

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-1) = ar_0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-2) = 1

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]", 0-3) = ar_0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-0) = 1

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-1) = ar_0

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-2) = 1

	S("evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]", 0-3) = ar_0

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-0) = 1

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-1) = ar_0

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-2) = 1

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= ar_3 ]", 0-3) = ar_0

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-0) = 1

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-1) = ar_0

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-2) = 1

	S("evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ ar_3 >= 1 ]", 0-3) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-0) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-1) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-2) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ 0 >= e + 1 ]", 0-3) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-0) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-1) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-2) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 /\\ e >= 1 ]", 0-3) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = 1

	S("evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0

	S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-0) = 1

	S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-1) = ar_0

	S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-2) = 1

	S("evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\\ ar_3 - 1 >= 0 /\\ ar_2 + ar_3 - 1 >= 0 /\\ ar_1 + ar_3 - 2 >= 0 /\\ ar_0 + ar_3 - 2 >= 0 /\\ -ar_0 + ar_3 >= 0 /\\ ar_2 >= 0 /\\ ar_1 + ar_2 - 1 >= 0 /\\ ar_0 + ar_2 - 1 >= 0 /\\ -ar_0 + ar_2 + 1 >= 0 /\\ ar_1 - 1 >= 0 /\\ ar_0 + ar_1 - 2 >= 0 /\\ -ar_0 + ar_1 >= 0 /\\ -ar_0 + 1 >= 0 /\\ ar_0 - 1 >= 0 ]", 0-3) = ar_0

	S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-0) = 1

	S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-1) = ar_0

	S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-2) = 1

	S("evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))", 0-3) = ar_0

	S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-0) = ar_0

	S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-1) = ar_1

	S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-2) = ar_2

	S("koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]", 0-3) = ar_3

orients the transitions

	evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

	evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]

weakly and the transitions

	evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

	evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]

strictly and produces the following problem:

6:	T:

		(Comp: 1, Cost: 0)               koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4start(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ]

		(Comp: 2, Cost: 1)               evalEx4returnin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4stop(ar_0, ar_1, ar_2, ar_3))

		(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 1, ar_3 - 1)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 ]

		(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ e >= 1 ]

		(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_3 - 1 >= 0 /\ ar_2 + ar_3 - 1 >= 0 /\ ar_1 + ar_3 - 2 >= 0 /\ ar_0 + ar_3 - 2 >= 0 /\ -ar_0 + ar_3 >= 0 /\ ar_2 >= 0 /\ ar_1 + ar_2 - 1 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ ar_1 - 1 >= 0 /\ ar_0 + ar_1 - 2 >= 0 /\ -ar_0 + ar_1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= e + 1 ]

		(Comp: 5*ar_0 + 2, Cost: 1)      evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ ar_3 >= 1 ]

		(Comp: 25*ar_0 + 12, Cost: 1)    evalEx4bb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(ar_2, ar_3, ar_2, ar_3)) [ ar_1 - ar_3 >= 0 /\ ar_2 >= 0 /\ ar_0 + ar_2 - 1 >= 0 /\ -ar_0 + ar_2 + 1 >= 0 /\ -ar_0 + 1 >= 0 /\ ar_0 - 1 >= 0 /\ 0 >= ar_3 ]

		(Comp: 2, Cost: 1)               evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= 2 ]

		(Comp: 2, Cost: 1)               evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4returnin(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ]

		(Comp: 25*ar_0 + 12, Cost: 1)    evalEx4bb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb2in(ar_0, ar_1, 0, ar_1)) [ ar_0 = 1 ]

		(Comp: 1, Cost: 1)               evalEx4entryin(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4bb4in(1, ar_0, ar_2, ar_3))

		(Comp: 1, Cost: 1)               evalEx4start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalEx4entryin(ar_0, ar_1, ar_2, ar_3))

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 75*ar_0 + 42



Time: 0.417 sec (SMT: 0.331 sec)


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

(2)
BOUNDS(1, n^1)

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalEx4start

      0: evalEx4start -> evalEx4entryin : [], cost: 1

      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      3: evalEx4bb4in -> evalEx4returnin : [ 0>=A ], cost: 1

      4: evalEx4bb4in -> evalEx4returnin : [ A>=2 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1

      7: evalEx4bb3in -> evalEx4bb1in : [ 0>=1+free ], cost: 1

      8: evalEx4bb3in -> evalEx4bb1in : [ free_1>=1 ], cost: 1

      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1

     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1

     11: evalEx4returnin -> evalEx4stop : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalEx4start

      0: evalEx4start -> evalEx4entryin : [], cost: 1

      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1

      7: evalEx4bb3in -> evalEx4bb1in : [ 0>=1+free ], cost: 1

      8: evalEx4bb3in -> evalEx4bb1in : [ free_1>=1 ], cost: 1

      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1

     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1



Simplified all rules, resulting in:

   Start location: evalEx4start

      0: evalEx4start -> evalEx4entryin : [], cost: 1

      1: evalEx4entryin -> evalEx4bb4in : A'=1, B'=A, [], cost: 1

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1

      8: evalEx4bb3in -> evalEx4bb1in : [], cost: 1

      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1

     10: evalEx4bb1in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

      6: evalEx4bb2in -> evalEx4bb3in : [ D>=1 ], cost: 1

      9: evalEx4bb3in -> evalEx4bb4in : A'=C, B'=D, [], cost: 1

     13: evalEx4bb3in -> evalEx4bb2in : C'=1, D'=-1+D, [], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2

     15: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=-1+D, [ D>=1 ], cost: 3



Accelerating simple loops of location 3.

   Accelerating the following rules:

     15: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=-1+D, [ D>=1 ], cost: 3



   Accelerated rule 15 with metering function D, yielding the new rule 16.

   Removing the simple loops: 15.



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

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2

     16: evalEx4bb2in -> evalEx4bb2in : C'=1, D'=0, [ D>=1 ], cost: 3*D



Chained accelerated rules (with incoming rules):

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

      2: evalEx4bb4in -> evalEx4bb2in : C'=0, D'=B, [ A==1 ], cost: 1

     17: evalEx4bb4in -> evalEx4bb2in : C'=1, D'=0, [ A==1 && B>=1 ], cost: 1+3*B

      5: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ 0>=D ], cost: 1

     14: evalEx4bb2in -> evalEx4bb4in : A'=C, B'=D, [ D>=1 ], cost: 2



Eliminated locations (on tree-shaped paths):

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

     18: evalEx4bb4in -> evalEx4bb4in : A'=0, B'=B, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2

     19: evalEx4bb4in -> evalEx4bb4in : A'=0, B'=B, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3

     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B

     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B



Accelerating simple loops of location 2.

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

   Accelerating the following rules:

     18: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2

     19: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3

     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B



   Accelerated rule 18 with metering function A, yielding the new rule 22.

   Accelerated rule 19 with metering function A, yielding the new rule 23.

   Found no metering function for rule 20.

   Removing the simple loops: 18 19.



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

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

     20: evalEx4bb4in -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A==1 && B>=1 ], cost: 2+3*B

     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B

     22: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && 0>=B ], cost: 2*A

     23: evalEx4bb4in -> evalEx4bb4in : A'=0, C'=0, D'=B, [ A==1 && B>=1 ], cost: 3*A



Chained accelerated rules (with incoming rules):

   Start location: evalEx4start

     12: evalEx4start -> evalEx4bb4in : A'=1, B'=A, [], cost: 2

     24: evalEx4start -> evalEx4bb4in : A'=1, B'=0, C'=1, D'=0, [ A>=1 ], cost: 4+3*A

     25: evalEx4start -> evalEx4bb4in : A'=0, B'=A, C'=0, D'=A, [ 0>=A ], cost: 4

     26: evalEx4start -> evalEx4bb4in : A'=0, B'=A, C'=0, D'=A, [ A>=1 ], cost: 5

     21: evalEx4bb4in -> [9] : [ A==1 && B>=1 ], cost: 1+3*B



Eliminated locations (on tree-shaped paths):

   Start location: evalEx4start

     27: evalEx4start -> [9] : A'=1, B'=A, [ A>=1 ], cost: 3+3*A

     28: evalEx4start -> [11] : [ A>=1 ], cost: 4+3*A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalEx4start

     28: evalEx4start -> [11] : [ A>=1 ], cost: 4+3*A



Computing asymptotic complexity for rule 28

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      4+3*A (+), A (+/+!) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {A==n}

      resulting limit problem:

      [solved]



   Solution:

      A / n

   Resulting cost 4+3*n has complexity: Poly(n^1)



Found new 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: 4+3*n

   Rule cost:   4+3*A

   Rule guard:  [ A>=1 ]



WORST_CASE(Omega(n^1),?)


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

(4)
BOUNDS(n^1, INF)