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Compl Integ Trans Syste 26843 pair #381744352
details
property
value
status
complete
benchmark
speedDis2.c.koat
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n033.star.cs.uiowa.edu
space
Flores-Montoya_16
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
2.61790895462 seconds
cpu usage
5.929578964
max memory
3.14679296E8
stage attributes
key
value
output-size
31194
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(n^1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 307 ms] (2) BOUNDS(1, n^1) (3) Loat Proof [FINISHED, 929 ms] (4) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_speedDis2_start(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb0_in(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_bb0_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_0(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_0(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_1(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_1(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_2(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_2(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_3(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_3(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_4(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_4(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_5(v__0, v__01, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_5(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v_x, v_z, v_n, v_x, v_z)) :|: TRUE eval_speedDis2_bb1_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb2_in(v__0, v__01, v_n, v_x, v_z)) :|: v__0 < v_n eval_speedDis2_bb1_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb3_in(v__0, v__01, v_n, v_x, v_z)) :|: v__0 >= v_n eval_speedDis2_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v__0 + 1, v__01, v_n, v_x, v_z)) :|: v__01 > v__0 eval_speedDis2_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v__0, v__01, v_n, v_x, v_z)) :|: v__01 > v__0 && v__01 <= v__0 eval_speedDis2_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v__0 + 1, v__01 + 1, v_n, v_x, v_z)) :|: v__01 <= v__0 && v__01 > v__0 eval_speedDis2_bb2_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_bb1_in(v__0, v__01 + 1, v_n, v_x, v_z)) :|: v__01 <= v__0 eval_speedDis2_bb3_in(v__0, v__01, v_n, v_x, v_z) -> Com_1(eval_speedDis2_stop(v__0, v__01, v_n, v_x, v_z)) :|: TRUE The start-symbols are:[eval_speedDis2_start_5] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 2*ar_3 + 4*ar_4 + 2*ar_1 + 13) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis2bb0in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis20(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis20(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis21(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis21(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis22(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis22(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis23(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis23(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis24(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis24(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis25(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis25(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_1, ar_1, ar_3, ar_3, ar_4)) (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_4 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_0 >= ar_4 ] (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] (Comp: ?, Cost: 1) evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 ] (Comp: ?, Cost: 1) evalspeedDis2bb3in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2stop(ar_0, ar_1, ar_2, ar_3, ar_4)) (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2start(ar_0, ar_1, ar_2, ar_3, ar_4)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Testing for reachability in the complexity graph removes the following transitions from problem 1: evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0, ar_1, ar_2, ar_3, ar_4)) [ ar_2 >= ar_0 + 1 /\ ar_0 >= ar_2 ] evalspeedDis2bb2in(ar_0, ar_1, ar_2, ar_3, ar_4) -> Com_1(evalspeedDis2bb1in(ar_0 + 1, ar_1, ar_2 + 1, ar_3, ar_4)) [ ar_0 >= ar_2 /\ ar_2 >= ar_0 + 1 ] We thus obtain the following problem:
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