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


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


WORST_CASE(Omega(n^1), O(n^1))
proof of /export/starexec/sandbox/benchmark/theBenchmark.koat
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 100 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 1734 ms]
(4) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalwcet1start(A, B, C, D) -> Com_1(evalwcet1entryin(A, B, C, D)) :|: TRUE
evalwcet1entryin(A, B, C, D) -> Com_1(evalwcet1bbin(A, 0, A, D)) :|: A >= 1
evalwcet1entryin(A, B, C, D) -> Com_1(evalwcet1returnin(A, B, C, D)) :|: 0 >= A
evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb1in(A, B, C, D)) :|: 0 >= E + 1
evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb1in(A, B, C, D)) :|: E >= 1
evalwcet1bbin(A, B, C, D) -> Com_1(evalwcet1bb4in(A, B, C, D)) :|: TRUE
evalwcet1bb1in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, 0)) :|: B + 1 >= A
evalwcet1bb1in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, B + 1)) :|: A >= B + 2
evalwcet1bb4in(A, B, C, D) -> Com_1(evalwcet1bb5in(A, B, C, D)) :|: 1 >= B
evalwcet1bb4in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, B - 1)) :|: B >= 2
evalwcet1bb5in(A, B, C, D) -> Com_1(evalwcet1bb6in(A, B, C, 0)) :|: TRUE
evalwcet1bb6in(A, B, C, D) -> Com_1(evalwcet1bbin(A, D, C - 1, D)) :|: C >= 2
evalwcet1bb6in(A, B, C, D) -> Com_1(evalwcet1returnin(A, B, C, D)) :|: 1 >= C
evalwcet1returnin(A, B, C, D) -> Com_1(evalwcet1stop(A, B, C, D)) :|: TRUE

The start-symbols are:[evalwcet1start_4]


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

(1) Koat Proof (FINISHED)
YES(?, 11*Ar_0 + 17)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]

		(Comp: ?, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

		(Comp: ?, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(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)    evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]

		(Comp: 1, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

		(Comp: ?, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalwcet1start) = 2

	Pol(evalwcet1entryin) = 2

	Pol(evalwcet1bbin) = 2

	Pol(evalwcet1returnin) = 1

	Pol(evalwcet1bb1in) = 2

	Pol(evalwcet1bb4in) = 2

	Pol(evalwcet1bb6in) = 2

	Pol(evalwcet1bb5in) = 2

	Pol(evalwcet1stop) = 0

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

	evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

strictly and produces the following problem:

3:	T:

		(Comp: 1, Cost: 1)    evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]

		(Comp: 1, Cost: 1)    evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

		(Comp: ?, Cost: 1)    evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

		(Comp: ?, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

		(Comp: ?, Cost: 1)    evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

		(Comp: ?, Cost: 1)    evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

		(Comp: ?, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

		(Comp: 2, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

		(Comp: 2, Cost: 1)    evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(evalwcet1bbin) = V_3

	Pol(evalwcet1bb4in) = V_3

	Pol(evalwcet1bb1in) = V_3

	Pol(evalwcet1bb6in) = V_3

	Pol(evalwcet1bb5in) = V_3

and size complexities

	S("koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(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(evalwcet1start(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(evalwcet1start(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(evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]", 0-3) = Ar_3

	S("evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0

	S("evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ?

	S("evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_0 + Ar_2

	S("evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ?

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]", 0-0) = Ar_0

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]", 0-1) = ?

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]", 0-2) = Ar_0

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]", 0-3) = ?

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]", 0-0) = Ar_0

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]", 0-1) = ?

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]", 0-2) = Ar_0

	S("evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]", 0-3) = ?

	S("evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))", 0-0) = Ar_0

	S("evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))", 0-1) = ?

	S("evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))", 0-2) = Ar_0

	S("evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))", 0-3) = 0

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]", 0-0) = Ar_0

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]", 0-1) = ?

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]", 0-2) = Ar_0

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]", 0-3) = ?

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]", 0-0) = Ar_0

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]", 0-1) = ?

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]", 0-2) = Ar_0

	S("evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]", 0-3) = ?

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]", 0-0) = Ar_0

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]", 0-1) = ?

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]", 0-2) = Ar_0

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]", 0-3) = ?

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]", 0-0) = Ar_0

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]", 0-1) = ?

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]", 0-2) = Ar_0

	S("evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]", 0-3) = 0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = ?

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = ?

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-0) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-1) = ?

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-2) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]", 0-3) = ?

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-0) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-1) = ?

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-2) = Ar_0

	S("evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]", 0-3) = ?

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-0) = Ar_0

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-1) = Ar_1

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-2) = Ar_2

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]", 0-3) = Ar_3

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]", 0-0) = Ar_0

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]", 0-1) = 0

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]", 0-2) = Ar_0

	S("evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]", 0-3) = Ar_3

	S("evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-0) = Ar_0

	S("evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-1) = Ar_1

	S("evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-2) = Ar_2

	S("evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))", 0-3) = Ar_3

orients the transitions

	evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

	evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

	evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

	evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

	evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

	evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

	evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

	evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

	evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

weakly and the transition

	evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

strictly and produces the following problem:

4:	T:

		(Comp: 1, Cost: 1)       evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)       evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]

		(Comp: 1, Cost: 1)       evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: ?, Cost: 1)       evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

		(Comp: ?, Cost: 1)       evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

		(Comp: ?, Cost: 1)       evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: ?, Cost: 1)       evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

		(Comp: ?, Cost: 1)       evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

		(Comp: ?, Cost: 1)       evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

		(Comp: ?, Cost: 1)       evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

		(Comp: ?, Cost: 1)       evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

		(Comp: Ar_0, Cost: 1)    evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

		(Comp: 2, Cost: 1)       evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

		(Comp: 2, Cost: 1)       evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 0)       koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 4 produces the following problem:

5:	T:

		(Comp: 1, Cost: 1)             evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 1)             evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, 0, Ar_0, Ar_3)) [ Ar_0 >= 1 ]

		(Comp: 1, Cost: 1)             evalwcet1entryin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= Ar_0 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 >= E + 1 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3)) [ E >= 1 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bbin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 2*Ar_0 + 2, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0)) [ Ar_1 + 1 >= Ar_0 ]

		(Comp: 2*Ar_0 + 2, Cost: 1)    evalwcet1bb1in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 + 1)) [ Ar_0 >= Ar_1 + 2 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_1 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bb4in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_1 - 1)) [ Ar_1 >= 2 ]

		(Comp: Ar_0 + 1, Cost: 1)      evalwcet1bb5in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bb6in(Ar_0, Ar_1, Ar_2, 0))

		(Comp: Ar_0, Cost: 1)          evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1bbin(Ar_0, Ar_3, Ar_2 - 1, Ar_3)) [ Ar_2 >= 2 ]

		(Comp: 2, Cost: 1)             evalwcet1bb6in(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3)) [ 1 >= Ar_2 ]

		(Comp: 2, Cost: 1)             evalwcet1returnin(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1stop(Ar_0, Ar_1, Ar_2, Ar_3))

		(Comp: 1, Cost: 0)             koat_start(Ar_0, Ar_1, Ar_2, Ar_3) -> Com_1(evalwcet1start(Ar_0, Ar_1, Ar_2, Ar_3)) [ 0 <= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 11*Ar_0 + 17



Time: 0.133 sec (SMT: 0.108 sec)


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

(2)
BOUNDS(1, n^1)

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalwcet1start

      0: evalwcet1start -> evalwcet1entryin : [], cost: 1

      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1

      2: evalwcet1entryin -> evalwcet1returnin : [ 0>=A ], cost: 1

      3: evalwcet1bbin -> evalwcet1bb1in : [ 0>=1+free ], cost: 1

      4: evalwcet1bbin -> evalwcet1bb1in : [ free_1>=1 ], cost: 1

      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1

      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1

      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1

      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1

      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1

     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1

     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1

     12: evalwcet1bb6in -> evalwcet1returnin : [ 1>=C ], cost: 1

     13: evalwcet1returnin -> evalwcet1stop : [], cost: 1



Checking for constant complexity:

   The following rule is satisfiable with cost >= 1, yielding constant complexity:

      0: evalwcet1start -> evalwcet1entryin : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalwcet1start

      0: evalwcet1start -> evalwcet1entryin : [], cost: 1

      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1

      3: evalwcet1bbin -> evalwcet1bb1in : [ 0>=1+free ], cost: 1

      4: evalwcet1bbin -> evalwcet1bb1in : [ free_1>=1 ], cost: 1

      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1

      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1

      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1

      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1

      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1

     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1

     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1



Simplified all rules, resulting in:

   Start location: evalwcet1start

      0: evalwcet1start -> evalwcet1entryin : [], cost: 1

      1: evalwcet1entryin -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 1

      4: evalwcet1bbin -> evalwcet1bb1in : [], cost: 1

      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1

      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1

      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1

      8: evalwcet1bb4in -> evalwcet1bb5in : [ 1>=B ], cost: 1

      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1

     10: evalwcet1bb5in -> evalwcet1bb6in : D'=0, [], cost: 1

     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalwcet1start

     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2

      4: evalwcet1bbin -> evalwcet1bb1in : [], cost: 1

      5: evalwcet1bbin -> evalwcet1bb4in : [], cost: 1

      6: evalwcet1bb1in -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 1

      7: evalwcet1bb1in -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 1

      9: evalwcet1bb4in -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 1

     15: evalwcet1bb4in -> evalwcet1bb6in : D'=0, [ 1>=B ], cost: 2

     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalwcet1start

     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2

     16: evalwcet1bbin -> evalwcet1bb6in : D'=0, [ 1+B>=A ], cost: 2

     17: evalwcet1bbin -> evalwcet1bb6in : D'=1+B, [ A>=2+B ], cost: 2

     18: evalwcet1bbin -> evalwcet1bb6in : D'=-1+B, [ B>=2 ], cost: 2

     19: evalwcet1bbin -> evalwcet1bb6in : D'=0, [ 1>=B ], cost: 3

     11: evalwcet1bb6in -> evalwcet1bbin : B'=D, C'=-1+C, [ C>=2 ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalwcet1start

     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2

     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3

     21: evalwcet1bbin -> evalwcet1bbin : B'=1+B, C'=-1+C, D'=1+B, [ A>=2+B && C>=2 ], cost: 3

     22: evalwcet1bbin -> evalwcet1bbin : B'=-1+B, C'=-1+C, D'=-1+B, [ B>=2 && C>=2 ], cost: 3

     23: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1>=B && C>=2 ], cost: 4



Accelerating simple loops of location 2.

   Accelerating the following rules:

     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3

     21: evalwcet1bbin -> evalwcet1bbin : B'=1+B, C'=-1+C, D'=1+B, [ A>=2+B && C>=2 ], cost: 3

     22: evalwcet1bbin -> evalwcet1bbin : B'=-1+B, C'=-1+C, D'=-1+B, [ B>=2 && C>=2 ], cost: 3

     23: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1>=B && C>=2 ], cost: 4



   Accelerated rule 20 with metering function -1+C (after strengthening guard), yielding the new rule 24.

   Found no metering function for rule 21.

   Accelerated rule 22 with metering function -1+C (after adding B>=C), yielding the new rule 25.

   Accelerated rule 22 with metering function -1+B (after adding B<=C), yielding the new rule 26.

   Accelerated rule 23 with metering function -1+C, yielding the new rule 27.

   Removing the simple loops: 22 23.



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

   Start location: evalwcet1start

     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2

     20: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=-1+C, D'=0, [ 1+B>=A && C>=2 ], cost: 3

     21: evalwcet1bbin -> evalwcet1bbin : B'=1+B, C'=-1+C, D'=1+B, [ A>=2+B && C>=2 ], cost: 3

     24: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=1, D'=0, [ 1+B>=A && C>=2 && 1>=A ], cost: -3+3*C

     25: evalwcet1bbin -> evalwcet1bbin : B'=1-C+B, C'=1, D'=1-C+B, [ B>=2 && C>=2 && B>=C ], cost: -3+3*C

     26: evalwcet1bbin -> evalwcet1bbin : B'=1, C'=1+C-B, D'=1, [ B>=2 && C>=2 && B<=C ], cost: -3+3*B

     27: evalwcet1bbin -> evalwcet1bbin : B'=0, C'=1, D'=0, [ 1>=B && C>=2 ], cost: -4+4*C



Chained accelerated rules (with incoming rules):

   Start location: evalwcet1start

     14: evalwcet1start -> evalwcet1bbin : B'=0, C'=A, [ A>=1 ], cost: 2

     28: evalwcet1start -> evalwcet1bbin : B'=1, C'=-1+A, D'=1, [ A>=2 ], cost: 5

     29: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A



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

   Start location: evalwcet1start

     29: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalwcet1start

     29: evalwcet1start -> evalwcet1bbin : B'=0, C'=1, D'=0, [ A>=2 ], cost: -2+4*A



Computing asymptotic complexity for rule 29

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      -1+A (+/+!), -2+4*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 -2+4*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: -2+4*n

   Rule cost:   -2+4*A

   Rule guard:  [ A>=2 ]



WORST_CASE(Omega(n^1),?)


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

(4)
BOUNDS(n^1, INF)