Compl Integ Trans Syste 26843 pair #381744601

details
property	value
status	complete
benchmark	rank3.c.koat
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n026.star.cs.uiowa.edu
space	Flores-Montoya_16
run statistics
property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	67.0338408947 seconds
cpu usage	98.161541482
max memory	7.09435392E8
stage attributes
key	value
output-size	39417
starexec-result	WORST_CASE(Omega(n^1), ?)
output
/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(Omega(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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty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(n^1, INF).

(0) CpxIntTrs
(1) Loat Proof [FINISHED, 3431 ms]
(2) BOUNDS(n^1, INF)


----------------------------------------

(0)
Obligation:
Complexity Int TRS consisting of the following rules:
eval_rank2_start(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb0_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_bb0_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_0(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_0(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_1(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_1(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_2(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_2(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_3(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_3(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_4(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_4(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_5(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_5(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_6(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_6(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_7(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_7(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_8(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_8(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_m, v_x_1, v_x_2, v_m, v_y_1, v_y_2)) :|: TRUE
eval_rank2_bb1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb2_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_x_0 >= 2
eval_rank2_bb1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb9_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_x_0 < 2
eval_rank2_bb2_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb3_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_0 - 1, v_x_2, v_y_0, v_y_0 + v_x_0 - 1, v_y_2)) :|: TRUE
eval_rank2_bb3_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb4_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_y_1 >= v_x_1 + 1
eval_rank2_bb3_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2__critedge_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_y_1 < v_x_1 + 1
eval_rank2_bb4_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_14(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_14(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_15(v_10, v_14, v_15, v_16, nondef_0, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_15(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb5_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_5 > 0
eval_rank2_15(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2__critedge_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_5 <= 0
eval_rank2_bb5_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb6_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_1, v_y_0, v_y_1, v_y_1 - 1)) :|: TRUE
eval_rank2_bb6_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb7_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_y_2 >= v_x_2 + 3
eval_rank2_bb6_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2__critedge1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_y_2 < v_x_2 + 3
eval_rank2_bb7_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_20(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_20(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_21(nondef_1, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_21(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb8_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_10 > 0
eval_rank2_21(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2__critedge1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: v_10 <= 0
eval_rank2_bb8_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb6_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2 + 1, v_y_0, v_y_1, v_y_2 - 2)) :|: TRUE
eval_rank2__critedge1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_26(v_10, v_y_2 - 1, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_26(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_27(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_27(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb3_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_2, v_x_2, v_y_0, v_14, v_y_2)) :|: TRUE
eval_rank2__critedge_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_29(v_10, v_14, v_x_1 - 1, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_29(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_30(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_30(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_31(v_10, v_14, v_15, v_y_1 - v_15, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_31(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_32(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE
eval_rank2_32(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_bb1_in(v_10, v_14, v_15, v_16, v_5, v_m, v_15, v_x_1, v_x_2, v_16, v_y_1, v_y_2)) :|: TRUE
eval_rank2_bb9_in(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2) -> Com_1(eval_rank2_stop(v_10, v_14, v_15, v_16, v_5, v_m, v_x_0, v_x_1, v_x_2, v_y_0, v_y_1, v_y_2)) :|: TRUE

The start-symbols are:[eval_rank2_start_12]


----------------------------------------

(1) Loat Proof (FINISHED)


### Pre-processing the ITS problem ###



Initial linear ITS problem

   Start location: evalrank2start

      0: evalrank2start -> evalrank2bb0in : [], cost: 1

      1: evalrank2bb0in -> evalrank20 : [], cost: 1

      2: evalrank20 -> evalrank21 : [], cost: 1

      3: evalrank21 -> evalrank22 : [], cost: 1

      4: evalrank22 -> evalrank23 : [], cost: 1

      5: evalrank23 -> evalrank24 : [], cost: 1

      6: evalrank24 -> evalrank25 : [], cost: 1

      7: evalrank25 -> evalrank26 : [], cost: 1

      8: evalrank26 -> evalrank27 : [], cost: 1

      9: evalrank27 -> evalrank28 : [], cost: 1

     10: evalrank28 -> evalrank2bb1in : A'=B, C'=B, [], cost: 1

     11: evalrank2bb1in -> evalrank2bb2in : [ A>=2 ], cost: 1
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