/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(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 1).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 49 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f11(100, O, 1, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE
f0(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f11(100, O, 0, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f23(A, B, 1, 1, 1, 100, O, 1, I, J, K, L, M, N)) :|: C >= 1 && C <= 1
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f23(A, B, 1, 1, 1, 100, O, 0, I, J, K, L, M, N)) :|: C >= 1 && C <= 1
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f26(A, B, C, D, H, F, G, H, 100, J, K, L, M, N)) :|: 0 >= H
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f26(A, B, C, D, H, F, G, H, 100, J, K, L, M, N)) :|: H >= 2
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f36(A, B, C, C, C, F, G, H, I, 100, K, L, M, N)) :|: 0 >= C
f11(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f36(A, B, C, C, C, F, G, H, I, 100, K, L, M, N)) :|: C >= 2
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, 1, F, G, 1, I, J, O, P, M, N)) :|: 0 >= 2 + O && H >= 1 && H <= 1
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, 1, F, G, 1, I, J, O, P, M, N)) :|: O >= 0 && H >= 1 && H <= 1
f23(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, 1, F, G, 1, I, J, -(1), L, 100, O)) :|: H >= 1 && H <= 1
f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: 0 >= O + 1
f36(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE
f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: 0 >= O + 1
f26(A, B, C, D, E, F, G, H, I, J, K, L, M, N) -> Com_1(f32(A, B, C, D, E, F, G, H, I, J, K, L, M, N)) :|: TRUE

The start-symbols are:[f0_14]


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(1) Koat2 Proof (FINISHED)
YES( ?, 15 {O(1)})



Initial Complexity Problem:

  Start:  f0  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7, Arg_8, Arg_9, Arg_10, Arg_11, Arg_12, Arg_13  

  Temp_Vars:  O, P  

  Locations:  f0, f11, f23, f26, f32, f36  

  Transitions:

  0: f0->f11

  1: f0->f11

  2: f11->f23

  3: f11->f23

  6: f11->f36

  7: f11->f36

  4: f23->f26

  5: f23->f26

  8: f23->f32

  9: f23->f32

  10: f23->f32

  13: f26->f32

  14: f26->f32

  11: f36->f32

  12: f36->f32  



Timebounds: 

  Overall timebound: 15 {O(1)}

  0: f0->f11: 1 {O(1)}

  1: f0->f11: 1 {O(1)}

  2: f11->f23: 1 {O(1)}

  3: f11->f23: 1 {O(1)}

  6: f11->f36: 1 {O(1)}

  7: f11->f36: 1 {O(1)}

  4: f23->f26: 1 {O(1)}

  5: f23->f26: 1 {O(1)}

  8: f23->f32: 1 {O(1)}

  9: f23->f32: 1 {O(1)}

  10: f23->f32: 1 {O(1)}

  13: f26->f32: 1 {O(1)}

  14: f26->f32: 1 {O(1)}

  11: f36->f32: 1 {O(1)}

  12: f36->f32: 1 {O(1)}



Costbounds:

  Overall costbound: 15 {O(1)}

  0: f0->f11: 1 {O(1)}

  1: f0->f11: 1 {O(1)}

  2: f11->f23: 1 {O(1)}

  3: f11->f23: 1 {O(1)}

  6: f11->f36: 1 {O(1)}

  7: f11->f36: 1 {O(1)}

  4: f23->f26: 1 {O(1)}

  5: f23->f26: 1 {O(1)}

  8: f23->f32: 1 {O(1)}

  9: f23->f32: 1 {O(1)}

  10: f23->f32: 1 {O(1)}

  13: f26->f32: 1 {O(1)}

  14: f26->f32: 1 {O(1)}

  11: f36->f32: 1 {O(1)}

  12: f36->f32: 1 {O(1)}



Sizebounds:

`Lower:

  

`Upper:

  


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(2)
BOUNDS(1, 1)