/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(?, 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(1, max(2 + -8 * Arg_2, 2 + -8 * Arg_0 + 8 * Arg_1, 10)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 143 ms]
(2) BOUNDS(1, max(2 + -8 * Arg_2, 2 + -8 * Arg_0 + 8 * Arg_1, 10))


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

The start-symbols are:[l0_3]


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(1) Koat2 Proof (FINISHED)
YES( ?, 2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {O(n)})



Initial Complexity Problem:

  Start:  l0  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  l0, l1  

  Transitions:

  0: l0->l1

  1: l1->l1  



Timebounds: 

  Overall timebound: 2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {O(n)}

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

  1: l1->l1: 1+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {O(n)}



Costbounds:

  Overall costbound: 2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {O(n)}

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

  1: l1->l1: 1+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {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)}

  1: l1->l1, Arg_0: 2+Arg_2 {O(n)}

  1: l1->l1, Arg_1: 1 {O(1)}

  1: l1->l1, Arg_2: Arg_2 {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)}

  1: l1->l1, Arg_0: 2^(1+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]))*((1+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]))*max([0, max([Arg_2, 1+Arg_2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])])])])+max([0, max([Arg_0, max([Arg_2, 1+Arg_2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])])])])])) {O(EXP)}

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

  1: l1->l1, Arg_2: 1+Arg_2+8*max([1, max([-(Arg_2), Arg_1-Arg_0])]) {O(n)}


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(2)
BOUNDS(1, max(2 + -8 * Arg_2, 2 + -8 * Arg_0 + 8 * Arg_1, 10))