/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 230 ms]
(2) BOUNDS(1, n^1)
(3) Loat Proof [FINISHED, 630 ms]
(4) BOUNDS(n^1, INF)


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

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_start_start(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb0_in(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_bb0_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_0(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_0(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_1(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_1(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_2(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_2(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_3(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_3(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_4(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_4(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_5(v__0, v__01, v_n, v_x, v_z)) :|: TRUE
eval_start_5(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE
eval_start_bb1_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb2_in(v__0, v__01, v_n, v_x, v_z)) :|: v__0 < v_n
eval_start_bb1_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb3_in(v__0, v__01, v_n, v_x, v_z)) :|: v__0 >= v_n
eval_start_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb1_in(v__0 + 1, v__01, v_n, v_x, v_z)) :|: v__01 > v__0
eval_start_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb1_in(v__0, v__01, v_n, v_x, v_z)) :|: v__01 > v__0 && v__01 <= v__0
eval_start_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb1_in(v__0 + 1, v__01 + 1, v_n, v_x, v_z)) :|: v__01 <= v__0 && v__01 > v__0
eval_start_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_bb1_in(v__0, v__01 + 1, v_n, v_x, v_z)) :|: v__01 <= v__0
eval_start_bb3_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_start_stop(v__0, v__01, v_n, v_x, v_z)) :|: TRUE

The start-symbols are:[eval_start_start_5]


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

(1) Koat Proof (FINISHED)
YES(?, 2*Ar_3 + 4*Ar_4 + 2*Ar_1 + 13)



Initial complexity problem:

1:	T:

		(Comp: ?, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(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(evalstartstart(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:

	evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 /\ Ar_0 >= Ar_2 ]

	evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 /\ Ar_2 >= Ar_0 + 1 ]

We thus obtain the following problem:

2:	T:

		(Comp: ?, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(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(evalstartstart(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)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(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(evalstartstart(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(evalstartbb3in) = 1

	Pol(evalstartstop) = 0

	Pol(evalstartbb2in) = 2

	Pol(evalstartbb1in) = 2

	Pol(evalstart5) = 2

	Pol(evalstart4) = 2

	Pol(evalstart3) = 2

	Pol(evalstart2) = 2

	Pol(evalstart1) = 2

	Pol(evalstart0) = 2

	Pol(evalstartbb0in) = 2

	Pol(evalstartstart) = 2

	Pol(koat_start) = 2

orients all transitions weakly and the transitions

	evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

	evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ]

strictly and produces the following problem:

4:	T:

		(Comp: 2, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ Ar_0 >= Ar_2 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_4 >= Ar_0 + 1 ]

		(Comp: 1, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(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(evalstartstart(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 4 to obtain the following invariants:

  For symbol evalstartbb1in: X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0

  For symbol evalstartbb2in: -X_2 + X_5 - 1 >= 0 /\ -X_1 + X_5 - 1 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0

  For symbol evalstartbb3in: X_1 - X_5 >= 0 /\ X_3 - X_4 >= 0 /\ X_1 - X_2 >= 0





This yielded the following problem:

5:	T:

		(Comp: 1, Cost: 0)    koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)    evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)    evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ]

		(Comp: 2, Cost: 1)    evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = -V_2 + V_5

	Pol(evalstartstart) = -V_2 + V_5

	Pol(evalstartbb0in) = -V_2 + V_5

	Pol(evalstart0) = -V_2 + V_5

	Pol(evalstart1) = -V_2 + V_5

	Pol(evalstart2) = -V_2 + V_5

	Pol(evalstart3) = -V_2 + V_5

	Pol(evalstart4) = -V_2 + V_5

	Pol(evalstart5) = -V_2 + V_5

	Pol(evalstartbb1in) = -V_1 + V_5

	Pol(evalstartbb2in) = -V_1 + V_5

	Pol(evalstartbb3in) = -V_1 + V_5

	Pol(evalstartstop) = -V_1 + V_5

orients all transitions weakly and the transition

	evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_2 >= Ar_0 + 1 ]

strictly and produces the following problem:

6:	T:

		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)              evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)              evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)              evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ]

		(Comp: Ar_1 + Ar_4, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_2 >= Ar_0 + 1 ]

		(Comp: ?, Cost: 1)              evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ]

		(Comp: 2, Cost: 1)              evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



A polynomial rank function with

	Pol(koat_start) = -V_4 + V_5

	Pol(evalstartstart) = -V_4 + V_5

	Pol(evalstartbb0in) = -V_4 + V_5

	Pol(evalstart0) = -V_4 + V_5

	Pol(evalstart1) = -V_4 + V_5

	Pol(evalstart2) = -V_4 + V_5

	Pol(evalstart3) = -V_4 + V_5

	Pol(evalstart4) = -V_4 + V_5

	Pol(evalstart5) = -V_4 + V_5

	Pol(evalstartbb1in) = -V_3 + V_5

	Pol(evalstartbb2in) = -V_3 + V_5

	Pol(evalstartbb3in) = -V_3 + V_5

	Pol(evalstartstop) = -V_3 + V_5

orients all transitions weakly and the transition

	evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ]

strictly and produces the following problem:

7:	T:

		(Comp: 1, Cost: 0)              koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)              evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)              evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: ?, Cost: 1)              evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)              evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ]

		(Comp: Ar_1 + Ar_4, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_2 >= Ar_0 + 1 ]

		(Comp: Ar_3 + Ar_4, Cost: 1)    evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ]

		(Comp: 2, Cost: 1)              evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



Repeatedly propagating knowledge in problem 7 produces the following problem:

8:	T:

		(Comp: 1, Cost: 0)                           koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ 0 <= 0 ]

		(Comp: 1, Cost: 1)                           evalstartstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstartbb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart0(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart3(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart4(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4))

		(Comp: 1, Cost: 1)                           evalstart5(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4))

		(Comp: Ar_3 + 2*Ar_4 + Ar_1 + 1, Cost: 1)    evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_4 >= Ar_0 + 1 ]

		(Comp: 2, Cost: 1)                           evalstartbb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_4 ]

		(Comp: Ar_1 + Ar_4, Cost: 1)                 evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0 + 1, Ar_1, Ar_2, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_2 >= Ar_0 + 1 ]

		(Comp: Ar_3 + Ar_4, Cost: 1)                 evalstartbb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartbb1in(Ar_0, Ar_1, Ar_2 + 1, Ar_3, Ar_4)) [ -Ar_1 + Ar_4 - 1 >= 0 /\ -Ar_0 + Ar_4 - 1 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 /\ Ar_0 >= Ar_2 ]

		(Comp: 2, Cost: 1)                           evalstartbb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4) -> Com_1(evalstartstop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4)) [ Ar_0 - Ar_4 >= 0 /\ Ar_2 - Ar_3 >= 0 /\ Ar_0 - Ar_1 >= 0 ]

	start location:	koat_start

	leaf cost:	0



Complexity upper bound 2*Ar_3 + 4*Ar_4 + 2*Ar_1 + 13



Time: 0.249 sec (SMT: 0.181 sec)


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

(2)
BOUNDS(1, n^1)

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

(3) Loat Proof (FINISHED)


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



Initial linear ITS problem

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstart4 : [], cost: 1

      6: evalstart4 -> evalstart5 : [], cost: 1

      7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1

      8: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1

      9: evalstartbb1in -> evalstartbb3in : [ A>=E ], cost: 1

     10: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=1+A ], cost: 1

     11: evalstartbb2in -> evalstartbb1in : [ C>=1+A && A>=C ], cost: 1

     12: evalstartbb2in -> evalstartbb1in : A'=1+A, C'=1+C, [ A>=C && C>=1+A ], cost: 1

     13: evalstartbb2in -> evalstartbb1in : C'=1+C, [ A>=C ], cost: 1

     14: evalstartbb3in -> evalstartstop : [], cost: 1



Checking for constant complexity:

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

      0: evalstartstart -> evalstartbb0in : [], cost: 1



Removed unreachable and leaf rules:

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstart4 : [], cost: 1

      6: evalstart4 -> evalstart5 : [], cost: 1

      7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1

      8: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1

     10: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=1+A ], cost: 1

     11: evalstartbb2in -> evalstartbb1in : [ C>=1+A && A>=C ], cost: 1

     12: evalstartbb2in -> evalstartbb1in : A'=1+A, C'=1+C, [ A>=C && C>=1+A ], cost: 1

     13: evalstartbb2in -> evalstartbb1in : C'=1+C, [ A>=C ], cost: 1



Removed rules with unsatisfiable guard:

   Start location: evalstartstart

      0: evalstartstart -> evalstartbb0in : [], cost: 1

      1: evalstartbb0in -> evalstart0 : [], cost: 1

      2: evalstart0 -> evalstart1 : [], cost: 1

      3: evalstart1 -> evalstart2 : [], cost: 1

      4: evalstart2 -> evalstart3 : [], cost: 1

      5: evalstart3 -> evalstart4 : [], cost: 1

      6: evalstart4 -> evalstart5 : [], cost: 1

      7: evalstart5 -> evalstartbb1in : A'=B, C'=D, [], cost: 1

      8: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1

     10: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=1+A ], cost: 1

     13: evalstartbb2in -> evalstartbb1in : C'=1+C, [ A>=C ], cost: 1



### Simplification by acceleration and chaining ###



Eliminated locations (on linear paths):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

      8: evalstartbb1in -> evalstartbb2in : [ E>=1+A ], cost: 1

     10: evalstartbb2in -> evalstartbb1in : A'=1+A, [ C>=1+A ], cost: 1

     13: evalstartbb2in -> evalstartbb1in : C'=1+C, [ A>=C ], cost: 1



Eliminated locations (on tree-shaped paths):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     22: evalstartbb1in -> evalstartbb1in : A'=1+A, [ E>=1+A && C>=1+A ], cost: 2

     23: evalstartbb1in -> evalstartbb1in : C'=1+C, [ E>=1+A && A>=C ], cost: 2



Accelerating simple loops of location 8.

   Accelerating the following rules:

     22: evalstartbb1in -> evalstartbb1in : A'=1+A, [ E>=1+A && C>=1+A ], cost: 2

     23: evalstartbb1in -> evalstartbb1in : C'=1+C, [ E>=1+A && A>=C ], cost: 2



   Found no metering function for rule 22.

   Accelerated rule 23 with metering function 1-C+A, yielding the new rule 24.

   Removing the simple loops: 23.



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

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     22: evalstartbb1in -> evalstartbb1in : A'=1+A, [ E>=1+A && C>=1+A ], cost: 2

     24: evalstartbb1in -> evalstartbb1in : C'=1+A, [ E>=1+A && A>=C ], cost: 2-2*C+2*A



Chained accelerated rules (with incoming rules):

   Start location: evalstartstart

     21: evalstartstart -> evalstartbb1in : A'=B, C'=D, [], cost: 8

     25: evalstartstart -> evalstartbb1in : A'=1+B, C'=D, [ E>=1+B && D>=1+B ], cost: 10

     26: evalstartstart -> evalstartbb1in : A'=B, C'=1+B, [ E>=1+B && B>=D ], cost: 10-2*D+2*B



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

   Start location: evalstartstart

     26: evalstartstart -> evalstartbb1in : A'=B, C'=1+B, [ E>=1+B && B>=D ], cost: 10-2*D+2*B



### Computing asymptotic complexity ###



Fully simplified ITS problem

   Start location: evalstartstart

     26: evalstartstart -> evalstartbb1in : A'=B, C'=1+B, [ E>=1+B && B>=D ], cost: 10-2*D+2*B



Computing asymptotic complexity for rule 26

   Solved the limit problem by the following transformations:

      Created initial limit problem:

      1-D+B (+/+!), E-B (+/+!), 10-2*D+2*B (+) [not solved]



      removing all constraints (solved by SMT)

      resulting limit problem: [solved]



      applying transformation rule (C) using substitution {D==-n,E==0,B==-1}

      resulting limit problem:

      [solved]



   Solution:

      D / -n

      E / 0

      B / -1

   Resulting cost 8+2*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: 8+2*n

   Rule cost:   10-2*D+2*B

   Rule guard:  [ E>=1+B && B>=D ]



WORST_CASE(Omega(n^1),?)


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

(4)
BOUNDS(n^1, INF)