/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty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, 0 ms]
(2) BOUNDS(1, 1)


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(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_relation1_start(v_x, v_y) -> Com_1(eval_relation1_bb0_in(v_x, v_y)) :|: TRUE
eval_relation1_bb0_in(v_x, v_y) -> Com_1(eval_relation1_0(v_x, v_y)) :|: TRUE
eval_relation1_0(v_x, v_y) -> Com_1(eval_relation1_1(v_x, v_y)) :|: TRUE
eval_relation1_1(v_x, v_y) -> Com_1(eval_relation1_2(v_x, v_y)) :|: TRUE
eval_relation1_2(v_x, v_y) -> Com_1(eval_relation1_3(v_x, v_y)) :|: TRUE
eval_relation1_3(v_x, v_y) -> Com_1(eval_relation1_4(v_x, v_y)) :|: TRUE
eval_relation1_4(v_x, v_y) -> Com_1(eval_relation1_5(v_x, v_y)) :|: TRUE
eval_relation1_5(v_x, v_y) -> Com_1(eval_relation1_bb1_in(v_x, v_y)) :|: TRUE
eval_relation1_bb1_in(v_x, v_y) -> Com_1(eval_relation1_6(v_x, v_y)) :|: TRUE
eval_relation1_6(v_x, v_y) -> Com_1(eval_relation1_7(v_x, v_y)) :|: TRUE
eval_relation1_7(v_x, v_y) -> Com_1(eval_relation1_bb2_in(v_x, v_y)) :|: TRUE
eval_relation1_bb2_in(v_x, v_y) -> Com_1(eval_relation1_stop(v_x, v_y)) :|: TRUE

The start-symbols are:[eval_relation1_start_2]


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(1) Koat2 Proof (FINISHED)
YES( ?, 12 {O(1)})



Initial Complexity Problem:

  Start:  evalrelation1start  

  Program_Vars:    

  Temp_Vars:    

  Locations:  evalrelation10, evalrelation11, evalrelation12, evalrelation13, evalrelation14, evalrelation15, evalrelation16, evalrelation17, evalrelation1bb0in, evalrelation1bb1in, evalrelation1bb2in, evalrelation1start, evalrelation1stop  

  Transitions:

  2: evalrelation10->evalrelation11

  3: evalrelation11->evalrelation12

  4: evalrelation12->evalrelation13

  5: evalrelation13->evalrelation14

  6: evalrelation14->evalrelation15

  7: evalrelation15->evalrelation1bb1in

  9: evalrelation16->evalrelation17

  10: evalrelation17->evalrelation1bb2in

  1: evalrelation1bb0in->evalrelation10

  8: evalrelation1bb1in->evalrelation16

  11: evalrelation1bb2in->evalrelation1stop

  0: evalrelation1start->evalrelation1bb0in  



Timebounds: 

  Overall timebound: 12 {O(1)}

  2: evalrelation10->evalrelation11: 1 {O(1)}

  3: evalrelation11->evalrelation12: 1 {O(1)}

  4: evalrelation12->evalrelation13: 1 {O(1)}

  5: evalrelation13->evalrelation14: 1 {O(1)}

  6: evalrelation14->evalrelation15: 1 {O(1)}

  7: evalrelation15->evalrelation1bb1in: 1 {O(1)}

  9: evalrelation16->evalrelation17: 1 {O(1)}

  10: evalrelation17->evalrelation1bb2in: 1 {O(1)}

  1: evalrelation1bb0in->evalrelation10: 1 {O(1)}

  8: evalrelation1bb1in->evalrelation16: 1 {O(1)}

  11: evalrelation1bb2in->evalrelation1stop: 1 {O(1)}

  0: evalrelation1start->evalrelation1bb0in: 1 {O(1)}



Costbounds:

  Overall costbound: 12 {O(1)}

  2: evalrelation10->evalrelation11: 1 {O(1)}

  3: evalrelation11->evalrelation12: 1 {O(1)}

  4: evalrelation12->evalrelation13: 1 {O(1)}

  5: evalrelation13->evalrelation14: 1 {O(1)}

  6: evalrelation14->evalrelation15: 1 {O(1)}

  7: evalrelation15->evalrelation1bb1in: 1 {O(1)}

  9: evalrelation16->evalrelation17: 1 {O(1)}

  10: evalrelation17->evalrelation1bb2in: 1 {O(1)}

  1: evalrelation1bb0in->evalrelation10: 1 {O(1)}

  8: evalrelation1bb1in->evalrelation16: 1 {O(1)}

  11: evalrelation1bb2in->evalrelation1stop: 1 {O(1)}

  0: evalrelation1start->evalrelation1bb0in: 1 {O(1)}



Sizebounds:

`Lower:

  

`Upper:

  


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(2)
BOUNDS(1, 1)