/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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(5 + -1 * Arg_0 + 2 * Arg_4 + -1 * Arg_6, 6)).

(0) CpxIntTrs
(1) Koat2 Proof [FINISHED, 1920 ms]
(2) BOUNDS(1, max(5 + -1 * Arg_0 + 2 * Arg_4 + -1 * Arg_6, 6))


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A >= 101 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
start(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: G >= E + 1 && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
start(A, B, C, D, E, F, G, H) -> Com_1(lbl71(A, H, C, D - 1, E, 1 + H, G, F)) :|: E >= G && 100 >= A && B >= C && B <= C && D >= E && D <= E && F >= G && F <= G && H >= A && H <= A
lbl71(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: A + G + E >= B + 102 + D && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
lbl71(A, B, C, D, E, F, G, H) -> Com_1(stop(A, B, C, D, E, F, G, H)) :|: B >= D && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
lbl71(A, B, C, D, E, F, G, H) -> Com_1(lbl71(A, H, C, D - 1, E, 1 + H, G, F)) :|: D >= B + 1 && 101 + B + D >= A + G + E && E >= 1 + D && 100 >= A && E >= G && 2 * D + 2 + B >= A + G + E && 100 >= B && F >= B + 1 && F <= B + 1 && H + B + 1 + D >= A + G + E && H + B + 1 + D <= A + G + E
start0(A, B, C, D, E, F, G, H) -> Com_1(start(A, C, C, E, E, G, G, A)) :|: TRUE

The start-symbols are:[start0_8]


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(1) Koat2 Proof (FINISHED)
YES( ?, max([6, 7+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)})



Initial Complexity Problem:

  Start:  start0  

  Program_Vars:  Arg_0, Arg_1, Arg_2, Arg_3, Arg_4, Arg_5, Arg_6, Arg_7  

  Temp_Vars:    

  Locations:  lbl71, start, start0, stop  

  Transitions:

  5: lbl71->lbl71

  3: lbl71->stop

  4: lbl71->stop

  2: start->lbl71

  0: start->stop

  1: start->stop

  6: start0->start  



Timebounds: 

  Overall timebound: max([6, 7+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)}

  3: lbl71->stop: 1 {O(1)}

  4: lbl71->stop: 1 {O(1)}

  5: lbl71->lbl71: max([0, 1+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)}

  0: start->stop: 1 {O(1)}

  1: start->stop: 1 {O(1)}

  2: start->lbl71: 1 {O(1)}

  6: start0->start: 1 {O(1)}



Costbounds:

  Overall costbound: max([6, 7+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)}

  3: lbl71->stop: 1 {O(1)}

  4: lbl71->stop: 1 {O(1)}

  5: lbl71->lbl71: max([0, 1+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)}

  0: start->stop: 1 {O(1)}

  1: start->stop: 1 {O(1)}

  2: start->lbl71: 1 {O(1)}

  6: start0->start: 1 {O(1)}



Sizebounds:

`Lower:

  3: lbl71->stop, Arg_0: Arg_0 {O(n)}

  3: lbl71->stop, Arg_1: min([Arg_0, min([Arg_6, min([Arg_6, -(-1-Arg_0)])])]) {O(n)}

  3: lbl71->stop, Arg_2: Arg_2 {O(n)}

  3: lbl71->stop, Arg_3: 100 {O(1)}

  3: lbl71->stop, Arg_4: 101 {O(1)}

  3: lbl71->stop, Arg_5: min([Arg_6, -(-1-Arg_0)]) {O(n)}

  3: lbl71->stop, Arg_6: Arg_6 {O(n)}

  3: lbl71->stop, Arg_7: 101 {O(1)}

  4: lbl71->stop, Arg_0: Arg_0 {O(n)}

  4: lbl71->stop, Arg_1: min([Arg_0, min([Arg_6, min([Arg_6, -(-1-Arg_0)])])]) {O(n)}

  4: lbl71->stop, Arg_2: Arg_2 {O(n)}

  4: lbl71->stop, Arg_3: min([-(1-Arg_4), -(1+-(Arg_4)+max([0, 1+-(Arg_0)-Arg_6+2*(-1+Arg_4)]))]) {O(n)}

  4: lbl71->stop, Arg_4: Arg_4 {O(n)}

  4: lbl71->stop, Arg_5: min([Arg_6, -(-1-Arg_0)]) {O(n)}

  4: lbl71->stop, Arg_6: Arg_6 {O(n)}

  4: lbl71->stop, Arg_7: min([Arg_6, min([Arg_6, -(-1-Arg_0)])]) {O(n)}

  5: lbl71->lbl71, Arg_0: Arg_0 {O(n)}

  5: lbl71->lbl71, Arg_1: min([Arg_6, min([Arg_6, -(-1-Arg_0)])]) {O(n)}

  5: lbl71->lbl71, Arg_2: Arg_2 {O(n)}

  5: lbl71->lbl71, Arg_3: -1+Arg_4-max([0, 1+-(Arg_0)-Arg_6+2*(-1+Arg_4)]) {O(n)}

  5: lbl71->lbl71, Arg_4: Arg_4 {O(n)}

  5: lbl71->lbl71, Arg_5: min([Arg_6, -(-1-Arg_0)]) {O(n)}

  5: lbl71->lbl71, Arg_6: Arg_6 {O(n)}

  5: lbl71->lbl71, Arg_7: min([Arg_6, -(-1-Arg_0)]) {O(n)}

  0: start->stop, Arg_0: 101 {O(1)}

  0: start->stop, Arg_1: Arg_2 {O(n)}

  0: start->stop, Arg_2: Arg_2 {O(n)}

  0: start->stop, Arg_3: Arg_4 {O(n)}

  0: start->stop, Arg_4: Arg_4 {O(n)}

  0: start->stop, Arg_5: Arg_6 {O(n)}

  0: start->stop, Arg_6: Arg_6 {O(n)}

  0: start->stop, Arg_7: 101 {O(1)}

  1: start->stop, Arg_0: Arg_0 {O(n)}

  1: start->stop, Arg_1: Arg_2 {O(n)}

  1: start->stop, Arg_2: Arg_2 {O(n)}

  1: start->stop, Arg_3: Arg_4 {O(n)}

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

  1: start->stop, Arg_5: Arg_6 {O(n)}

  1: start->stop, Arg_6: Arg_6 {O(n)}

  1: start->stop, Arg_7: Arg_0 {O(n)}

  2: start->lbl71, Arg_0: Arg_0 {O(n)}

  2: start->lbl71, Arg_1: Arg_0 {O(n)}

  2: start->lbl71, Arg_2: Arg_2 {O(n)}

  2: start->lbl71, Arg_3: -1+Arg_4 {O(n)}

  2: start->lbl71, Arg_4: Arg_4 {O(n)}

  2: start->lbl71, Arg_5: 1+Arg_0 {O(n)}

  2: start->lbl71, Arg_6: Arg_6 {O(n)}

  2: start->lbl71, Arg_7: Arg_6 {O(n)}

  6: start0->start, Arg_0: Arg_0 {O(n)}

  6: start0->start, Arg_1: Arg_2 {O(n)}

  6: start0->start, Arg_2: Arg_2 {O(n)}

  6: start0->start, Arg_3: Arg_4 {O(n)}

  6: start0->start, Arg_4: Arg_4 {O(n)}

  6: start0->start, Arg_5: Arg_6 {O(n)}

  6: start0->start, Arg_6: Arg_6 {O(n)}

  6: start0->start, Arg_7: Arg_0 {O(n)}

`Upper:

  3: lbl71->stop, Arg_0: 100 {O(1)}

  3: lbl71->stop, Arg_1: 100 {O(1)}

  3: lbl71->stop, Arg_2: Arg_2 {O(n)}

  3: lbl71->stop, Arg_3: -1+Arg_4 {O(n)}

  3: lbl71->stop, Arg_4: Arg_4 {O(n)}

  3: lbl71->stop, Arg_5: 101 {O(1)}

  3: lbl71->stop, Arg_6: Arg_6 {O(n)}

  3: lbl71->stop, Arg_7: max([101, Arg_6]) {O(n)}

  4: lbl71->stop, Arg_0: 100 {O(1)}

  4: lbl71->stop, Arg_1: 100 {O(1)}

  4: lbl71->stop, Arg_2: Arg_2 {O(n)}

  4: lbl71->stop, Arg_3: 100 {O(1)}

  4: lbl71->stop, Arg_4: Arg_4 {O(n)}

  4: lbl71->stop, Arg_5: 101 {O(1)}

  4: lbl71->stop, Arg_6: Arg_6 {O(n)}

  4: lbl71->stop, Arg_7: 101 {O(1)}

  5: lbl71->lbl71, Arg_0: 100 {O(1)}

  5: lbl71->lbl71, Arg_1: 100 {O(1)}

  5: lbl71->lbl71, Arg_2: Arg_2 {O(n)}

  5: lbl71->lbl71, Arg_3: -1+Arg_4 {O(n)}

  5: lbl71->lbl71, Arg_4: Arg_4 {O(n)}

  5: lbl71->lbl71, Arg_5: 101 {O(1)}

  5: lbl71->lbl71, Arg_6: Arg_6 {O(n)}

  5: lbl71->lbl71, Arg_7: 101 {O(1)}

  0: start->stop, Arg_0: Arg_0 {O(n)}

  0: start->stop, Arg_1: Arg_2 {O(n)}

  0: start->stop, Arg_2: Arg_2 {O(n)}

  0: start->stop, Arg_3: Arg_4 {O(n)}

  0: start->stop, Arg_4: Arg_4 {O(n)}

  0: start->stop, Arg_5: Arg_6 {O(n)}

  0: start->stop, Arg_6: Arg_6 {O(n)}

  0: start->stop, Arg_7: Arg_0 {O(n)}

  1: start->stop, Arg_0: Arg_0 {O(n)}

  1: start->stop, Arg_1: Arg_2 {O(n)}

  1: start->stop, Arg_2: Arg_2 {O(n)}

  1: start->stop, Arg_3: Arg_4 {O(n)}

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

  1: start->stop, Arg_5: Arg_6 {O(n)}

  1: start->stop, Arg_6: Arg_6 {O(n)}

  1: start->stop, Arg_7: Arg_0 {O(n)}

  2: start->lbl71, Arg_0: 100 {O(1)}

  2: start->lbl71, Arg_1: 100 {O(1)}

  2: start->lbl71, Arg_2: Arg_2 {O(n)}

  2: start->lbl71, Arg_3: -1+Arg_4 {O(n)}

  2: start->lbl71, Arg_4: Arg_4 {O(n)}

  2: start->lbl71, Arg_5: 101 {O(1)}

  2: start->lbl71, Arg_6: Arg_6 {O(n)}

  2: start->lbl71, Arg_7: Arg_6 {O(n)}

  6: start0->start, Arg_0: Arg_0 {O(n)}

  6: start0->start, Arg_1: Arg_2 {O(n)}

  6: start0->start, Arg_2: Arg_2 {O(n)}

  6: start0->start, Arg_3: Arg_4 {O(n)}

  6: start0->start, Arg_4: Arg_4 {O(n)}

  6: start0->start, Arg_5: Arg_6 {O(n)}

  6: start0->start, Arg_6: Arg_6 {O(n)}

  6: start0->start, Arg_7: Arg_0 {O(n)}


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(2)
BOUNDS(1, max(5 + -1 * Arg_0 + 2 * Arg_4 + -1 * Arg_6, 6))