/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(3, 104 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 441 ms]
(2) BOUNDS(1, max(3, 104 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalterminatestart(A, B, C) -> Com_1(evalterminateentryin(A, B, C)) :|: TRUE
evalterminateentryin(A, B, C) -> Com_1(evalterminatebb1in(B, A, C)) :|: TRUE
evalterminatebb1in(A, B, C) -> Com_1(evalterminatebbin(A, B, C)) :|: 100 >= B && A >= C
evalterminatebb1in(A, B, C) -> Com_1(evalterminatereturnin(A, B, C)) :|: B >= 101
evalterminatebb1in(A, B, C) -> Com_1(evalterminatereturnin(A, B, C)) :|: C >= A + 1
evalterminatebbin(A, B, C) -> Com_1(evalterminatebb1in(A - 1, C, B + 1)) :|: TRUE
evalterminatereturnin(A, B, C) -> Com_1(evalterminatestop(A, B, C)) :|: TRUE

The start-symbols are:[evalterminatestart_3]


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(1) Koat2 Proof (FINISHED)
YES( ?, 3+max([0, 101+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  evalterminatestart  

  Program_Vars:  Arg_0, Arg_1, Arg_2  

  Temp_Vars:    

  Locations:  evalterminatebb1in, evalterminatebbin, evalterminateentryin, evalterminatereturnin, evalterminatestart, evalterminatestop  

  Transitions:

  2: evalterminatebb1in->evalterminatebbin

  3: evalterminatebb1in->evalterminatereturnin

  4: evalterminatebb1in->evalterminatereturnin

  5: evalterminatebbin->evalterminatebb1in

  1: evalterminateentryin->evalterminatebb1in

  6: evalterminatereturnin->evalterminatestop

  0: evalterminatestart->evalterminateentryin  



Timebounds: 

  Overall timebound: 3+max([0, 101+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  2: evalterminatebb1in->evalterminatebbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}

  4: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}

  5: evalterminatebbin->evalterminatebb1in: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  1: evalterminateentryin->evalterminatebb1in: 1 {O(1)}

  6: evalterminatereturnin->evalterminatestop: 1 {O(1)}

  0: evalterminatestart->evalterminateentryin: 1 {O(1)}



Costbounds:

  Overall costbound: 3+max([0, 101+Arg_1+-(Arg_2)-Arg_0])+max([2, 103+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  2: evalterminatebb1in->evalterminatebbin: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}

  4: evalterminatebb1in->evalterminatereturnin: 1 {O(1)}

  5: evalterminatebbin->evalterminatebb1in: max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  1: evalterminateentryin->evalterminatebb1in: 1 {O(1)}

  6: evalterminatereturnin->evalterminatestop: 1 {O(1)}

  0: evalterminatestart->evalterminateentryin: 1 {O(1)}



Sizebounds:

`Lower:

  2: evalterminatebb1in->evalterminatebbin, Arg_0: Arg_1-max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  2: evalterminatebb1in->evalterminatebbin, Arg_1: min([Arg_2, Arg_0]) {O(n)}

  2: evalterminatebb1in->evalterminatebbin, Arg_2: min([Arg_2, Arg_0]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 101+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_1: 101 {O(1)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 101+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_1: min([Arg_0, min([Arg_2, Arg_0])]) {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_0: Arg_1-max([0, 101+Arg_1+-(Arg_2)-Arg_0]) {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_1: min([Arg_2, Arg_0]) {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_2: min([Arg_2, Arg_0]) {O(n)}

  1: evalterminateentryin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}

  1: evalterminateentryin->evalterminatebb1in, Arg_1: Arg_0 {O(n)}

  1: evalterminateentryin->evalterminatebb1in, Arg_2: Arg_2 {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_0: min([Arg_1, -(-(Arg_1)+max([0, 101+Arg_1+-(Arg_2)-Arg_0]))]) {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_1: min([101, min([Arg_2, Arg_0])]) {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_2: min([Arg_2, min([Arg_2, Arg_0])]) {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_0: Arg_0 {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_1: Arg_1 {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_2: Arg_2 {O(n)}

`Upper:

  2: evalterminatebb1in->evalterminatebbin, Arg_0: Arg_1 {O(n)}

  2: evalterminatebb1in->evalterminatebbin, Arg_1: 100 {O(1)}

  2: evalterminatebb1in->evalterminatebbin, Arg_2: max([101, Arg_2]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_0: Arg_1 {O(n)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}

  3: evalterminatebb1in->evalterminatereturnin, Arg_2: max([101, Arg_2]) {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_0: Arg_1 {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}

  4: evalterminatebb1in->evalterminatereturnin, Arg_2: max([101, Arg_2]) {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_1: max([101, Arg_2]) {O(n)}

  5: evalterminatebbin->evalterminatebb1in, Arg_2: 101 {O(1)}

  1: evalterminateentryin->evalterminatebb1in, Arg_0: Arg_1 {O(n)}

  1: evalterminateentryin->evalterminatebb1in, Arg_1: Arg_0 {O(n)}

  1: evalterminateentryin->evalterminatebb1in, Arg_2: Arg_2 {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_0: Arg_1 {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_1: max([101, max([Arg_0, Arg_2])]) {O(n)}

  6: evalterminatereturnin->evalterminatestop, Arg_2: max([101, Arg_2]) {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_0: Arg_0 {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_1: Arg_1 {O(n)}

  0: evalterminatestart->evalterminateentryin, Arg_2: Arg_2 {O(n)}


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(2)
BOUNDS(1, max(3, 104 + -1 * Arg_0 + Arg_1 + -1 * Arg_2) + max(2, 103 + -1 * Arg_0 + Arg_1 + -1 * Arg_2))