/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(?, 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, max(357 + 355 * Arg_4, 357 + 355 * Arg_2, 357 + 355 * Arg_3, 357, 2 + 355 * Arg_0, 357 + 355 * Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 254 ms]
(2) BOUNDS(1, max(357 + 355 * Arg_4, 357 + 355 * Arg_2, 357 + 355 * Arg_3, 357, 2 + 355 * Arg_0, 357 + 355 * Arg_1))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
l0(A, B, C, D, E) -> Com_1(l1(A, B, C, D, E)) :|: TRUE
l1(A, B, C, D, E) -> Com_1(l1(A + B, B + C, C + D, D + E, E - 1)) :|: A >= 1

The start-symbols are:[l0_5]


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(1) Koat2 Proof (FINISHED)
YES( ?, 2+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)})



Initial Complexity Problem:

  Start:  l0  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4  

  Temp_Vars:    

  Locations:  l0, l1  

  Transitions:

  0: l0->l1

  1: l1->l1  



Timebounds: 

  Overall timebound: 2+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)}

  0: l0->l1: 1 {O(1)}

  1: l1->l1: 1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)}



Costbounds:

  Overall costbound: 2+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)}

  0: l0->l1: 1 {O(1)}

  1: l1->l1: 1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)}



Sizebounds:

`Lower:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  0: l0->l1, Arg_3: Arg_3 {O(n)}

  0: l0->l1, Arg_4: Arg_4 {O(n)}

  1: l1->l1, Arg_0: min([-(-1+(1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_2), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])+max([-(Arg_2), max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])])])+max([-(Arg_1), max([-(Arg_2), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])+max([-(Arg_2), max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])])])), -(-1-Arg_1)]) {O(n^4)}

  1: l1->l1, Arg_1: min([Arg_1, min([Arg_2, -((1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])+max([-(Arg_2), max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])]))])])+(-1+-355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_2), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])+max([-(Arg_2), max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])])])]) {O(n^4)}

  1: l1->l1, Arg_2: min([Arg_2, min([Arg_3, -((1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])]))])])+(-1+-355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_3), (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])+max([-(Arg_3), max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])])])]) {O(n^3)}

  1: l1->l1, Arg_3: min([Arg_3, min([Arg_4, -(1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))])])+(-1+-355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([-(Arg_4), 1+-(Arg_4)+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])])])]) {O(n^2)}

  1: l1->l1, Arg_4: -1+Arg_4+-355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]) {O(n)}

`Upper:

  0: l0->l1, Arg_0: Arg_0 {O(n)}

  0: l0->l1, Arg_1: Arg_1 {O(n)}

  0: l0->l1, Arg_2: Arg_2 {O(n)}

  0: l0->l1, Arg_3: Arg_3 {O(n)}

  0: l0->l1, Arg_4: Arg_4 {O(n)}

  1: l1->l1, Arg_0: (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_1, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])])+max([Arg_1, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])])])])+max([Arg_0, max([Arg_1, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])])+max([Arg_1, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])])])]) {O(n^5)}

  1: l1->l1, Arg_1: (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])])+max([Arg_1, max([Arg_2, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])])]) {O(n^4)}

  1: l1->l1, Arg_2: (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])])+max([Arg_2, max([Arg_3, (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])])])]) {O(n^3)}

  1: l1->l1, Arg_3: (1+355*max([1, max([Arg_0, max([1+Arg_4, max([1+Arg_3, max([1+Arg_2, 1+Arg_1])])])])]))*max([0, Arg_4])+max([Arg_4, max([Arg_3, Arg_4])]) {O(n^2)}

  1: l1->l1, Arg_4: Arg_4 {O(n)}


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(2)
BOUNDS(1, max(357 + 355 * Arg_4, 357 + 355 * Arg_2, 357 + 355 * Arg_3, 357, 2 + 355 * Arg_0, 357 + 355 * Arg_1))