/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty


The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, max(5, 5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 869 ms]
(2) BOUNDS(1, max(5, 5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
evalfstart(A, B) -> Com_1(evalfentryin(A, B)) :|: TRUE
evalfentryin(A, B) -> Com_1(evalfbb3in(B, A)) :|: TRUE
evalfbb3in(A, B) -> Com_1(evalfbbin(A, B)) :|: B >= 1 && 254 >= B
evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: 0 >= B
evalfbb3in(A, B) -> Com_1(evalfreturnin(A, B)) :|: B >= 255
evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: 0 >= A + 1
evalfbbin(A, B) -> Com_1(evalfbb1in(A, B)) :|: A >= 1
evalfbbin(A, B) -> Com_1(evalfbb2in(A, B)) :|: A >= 0 && A <= 0
evalfbb1in(A, B) -> Com_1(evalfbb3in(A, B + 1)) :|: TRUE
evalfbb2in(A, B) -> Com_1(evalfbb3in(A, B - 1)) :|: TRUE
evalfreturnin(A, B) -> Com_1(evalfstop(A, B)) :|: TRUE

The start-symbols are:[evalfstart_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)})



Initial Complexity Problem:

  Start:  evalfstart  

  Program_Vars:  Arg_0, Arg_1  

  Temp_Vars:    

  Locations:  evalfbb1in, evalfbb2in, evalfbb3in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop  

  Transitions:

  evalfbb1in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1+1):|:Arg_1 <= 254 && 1 <= Arg_1

  evalfbb2in(Arg_0,Arg_1) -> evalfbb3in(Arg_0,Arg_1-1):|:Arg_1 <= 254 && Arg_1 <= 254+Arg_0 && Arg_0+Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0+Arg_1 && 1+Arg_0 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0

  evalfbb3in(Arg_0,Arg_1) -> evalfbbin(Arg_0,Arg_1):|:1 <= Arg_1 && Arg_1 <= 254

  evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:Arg_1 <= 0

  evalfbb3in(Arg_0,Arg_1) -> evalfreturnin(Arg_0,Arg_1):|:255 <= Arg_1

  evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0+1 <= 0

  evalfbbin(Arg_0,Arg_1) -> evalfbb1in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && 1 <= Arg_0

  evalfbbin(Arg_0,Arg_1) -> evalfbb2in(Arg_0,Arg_1):|:Arg_1 <= 254 && 1 <= Arg_1 && Arg_0 <= 0 && 0 <= Arg_0

  evalfentryin(Arg_0,Arg_1) -> evalfbb3in(Arg_1,Arg_0):|:

  evalfreturnin(Arg_0,Arg_1) -> evalfstop(Arg_0,Arg_1):|:

  evalfstart(Arg_0,Arg_1) -> evalfentryin(Arg_0,Arg_1):|:  



Timebounds: 

  Overall timebound: 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}

  8: evalfbb1in->evalfbb3in: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}

  9: evalfbb2in->evalfbb3in: 254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0])) {O(n)}

  2: evalfbb3in->evalfbbin: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}

  3: evalfbb3in->evalfreturnin: 1 {O(1)}

  4: evalfbb3in->evalfreturnin: 1 {O(1)}

  5: evalfbbin->evalfbb1in: max([0, -64517*Arg_1+-254*Arg_0]) {O(n)}

  6: evalfbbin->evalfbb1in: max([0, 257049*Arg_1+-1012*Arg_0]) {O(n)}

  7: evalfbbin->evalfbb2in: max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}

  1: evalfentryin->evalfbb3in: 1 {O(1)}

  10: evalfreturnin->evalfstop: 1 {O(1)}

  0: evalfstart->evalfentryin: 1 {O(1)}



Costbounds:

  Overall costbound: 5+2*64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 255-Arg_0])+max([0, 257049*Arg_1+-1012*Arg_0])+max([0, 255-Arg_0])+max([0, -64517*Arg_1+-254*Arg_0])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}

  8: evalfbb1in->evalfbb3in: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}

  9: evalfbb2in->evalfbb3in: 254*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0])) {O(n)}

  2: evalfbb3in->evalfbbin: 64770*(max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]))+max([0, 255-Arg_0]) {O(n)}

  3: evalfbb3in->evalfreturnin: 1 {O(1)}

  4: evalfbb3in->evalfreturnin: 1 {O(1)}

  5: evalfbbin->evalfbb1in: max([0, -64517*Arg_1+-254*Arg_0]) {O(n)}

  6: evalfbbin->evalfbb1in: max([0, 257049*Arg_1+-1012*Arg_0]) {O(n)}

  7: evalfbbin->evalfbb2in: max([0, 129032*(257049*Arg_1+-1012*Arg_0)])+max([0, 129032*(-64517*Arg_1+-254*Arg_0)])+max([0, 254*Arg_0]) {O(n)}

  1: evalfentryin->evalfbb3in: 1 {O(1)}

  10: evalfreturnin->evalfstop: 1 {O(1)}

  0: evalfstart->evalfentryin: 1 {O(1)}



Sizebounds:

`Lower:

  8: evalfbb1in->evalfbb3in, Arg_0: min([0, Arg_1]) {O(n)}

  8: evalfbb1in->evalfbb3in, Arg_1: 2 {O(1)}

  9: evalfbb2in->evalfbb3in, Arg_0: 0 {O(1)}

  9: evalfbb2in->evalfbb3in, Arg_1: 0 {O(1)}

  2: evalfbb3in->evalfbbin, Arg_0: min([0, Arg_1]) {O(n)}

  2: evalfbb3in->evalfbbin, Arg_1: 1 {O(1)}

  3: evalfbb3in->evalfreturnin, Arg_0: min([0, Arg_1]) {O(n)}

  3: evalfbb3in->evalfreturnin, Arg_1: min([0, Arg_0]) {O(n)}

  4: evalfbb3in->evalfreturnin, Arg_0: min([0, Arg_1]) {O(n)}

  4: evalfbb3in->evalfreturnin, Arg_1: 255 {O(1)}

  5: evalfbbin->evalfbb1in, Arg_0: min([0, Arg_1]) {O(n)}

  5: evalfbbin->evalfbb1in, Arg_1: 1 {O(1)}

  6: evalfbbin->evalfbb1in, Arg_0: 1 {O(1)}

  6: evalfbbin->evalfbb1in, Arg_1: 1 {O(1)}

  7: evalfbbin->evalfbb2in, Arg_0: 0 {O(1)}

  7: evalfbbin->evalfbb2in, Arg_1: 1 {O(1)}

  1: evalfentryin->evalfbb3in, Arg_0: Arg_1 {O(n)}

  1: evalfentryin->evalfbb3in, Arg_1: Arg_0 {O(n)}

  10: evalfreturnin->evalfstop, Arg_0: min([0, Arg_1]) {O(n)}

  10: evalfreturnin->evalfstop, Arg_1: min([255, min([0, Arg_0])]) {O(n)}

  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}

  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}

`Upper:

  8: evalfbb1in->evalfbb3in, Arg_0: max([0, Arg_1]) {O(n)}

  8: evalfbb1in->evalfbb3in, Arg_1: 255 {O(1)}

  9: evalfbb2in->evalfbb3in, Arg_0: 0 {O(1)}

  9: evalfbb2in->evalfbb3in, Arg_1: 253 {O(1)}

  2: evalfbb3in->evalfbbin, Arg_0: max([0, Arg_1]) {O(n)}

  2: evalfbb3in->evalfbbin, Arg_1: 254 {O(1)}

  3: evalfbb3in->evalfreturnin, Arg_0: max([0, Arg_1]) {O(n)}

  3: evalfbb3in->evalfreturnin, Arg_1: 0 {O(1)}

  4: evalfbb3in->evalfreturnin, Arg_0: max([0, Arg_1]) {O(n)}

  4: evalfbb3in->evalfreturnin, Arg_1: max([255, Arg_0]) {O(n)}

  5: evalfbbin->evalfbb1in, Arg_0: -1 {O(1)}

  5: evalfbbin->evalfbb1in, Arg_1: 254 {O(1)}

  6: evalfbbin->evalfbb1in, Arg_0: max([0, Arg_1]) {O(n)}

  6: evalfbbin->evalfbb1in, Arg_1: 254 {O(1)}

  7: evalfbbin->evalfbb2in, Arg_0: 0 {O(1)}

  7: evalfbbin->evalfbb2in, Arg_1: 254 {O(1)}

  1: evalfentryin->evalfbb3in, Arg_0: Arg_1 {O(n)}

  1: evalfentryin->evalfbb3in, Arg_1: Arg_0 {O(n)}

  10: evalfreturnin->evalfstop, Arg_0: max([0, Arg_1]) {O(n)}

  10: evalfreturnin->evalfstop, Arg_1: max([255, Arg_0]) {O(n)}

  0: evalfstart->evalfentryin, Arg_0: Arg_0 {O(n)}

  0: evalfstart->evalfentryin, Arg_1: Arg_1 {O(n)}


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(2)
BOUNDS(1, max(5, 5 + -16948680941280 * Arg_0 + 4304981706793560 * Arg_1) + nat(-4253917943760 * Arg_0 + -1080511905423480 * Arg_1) + nat(32967930 * Arg_0) + nat(510 + -2 * Arg_0) + nat(-1012 * Arg_0 + 257049 * Arg_1) + nat(-254 * Arg_0 + -64517 * Arg_1))