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Complexity_C_Integer 2019-03-21 04.38 pair #429988888
details
property
value
status
complete
benchmark
jama_ex6.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
ABC
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.6351 seconds
cpu usage
2.58527
user time
2.38656
system time
0.198716
max virtual memory
1.828276E7
max residence set size
185224.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^4))
output
2.11/1.59 WORST_CASE(?, O(n^4)) 2.11/1.60 proof of /export/starexec/sandbox/output/output_files/bench.koat 2.11/1.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.11/1.60 2.11/1.60 2.11/1.60 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^4). 2.11/1.60 2.11/1.60 (0) CpxIntTrs 2.11/1.60 (1) Koat Proof [FINISHED, 361 ms] 2.11/1.60 (2) BOUNDS(1, n^4) 2.11/1.60 2.11/1.60 2.11/1.60 ---------------------------------------- 2.11/1.60 2.11/1.60 (0) 2.11/1.60 Obligation: 2.11/1.60 Complexity Int TRS consisting of the following rules: 2.11/1.60 eval_jama_ex6_start(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb0_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb1_in(v_a, v_b, v_c, v_d, v_a, v_j.0, v_k.0)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_c, v_k.0)) :|: v_i.0 <= v_b 2.11/1.60 eval_jama_ex6_bb1_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb8_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: v_i.0 > v_b 2.11/1.60 eval_jama_ex6_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: v_j.0 <= v_d 2.11/1.60 eval_jama_ex6_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb7_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: v_j.0 > v_d 2.11/1.60 eval_jama_ex6_bb3_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_i.0 - v_j.0)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: v_k.0 <= v_i.0 + v_j.0 2.11/1.60 eval_jama_ex6_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb6_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: v_k.0 > v_i.0 + v_j.0 2.11/1.60 eval_jama_ex6_bb5_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb4_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0 + 1)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb6_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb2_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0 + 1, v_k.0)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb7_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_bb1_in(v_a, v_b, v_c, v_d, v_i.0 + 1, v_j.0, v_k.0)) :|: TRUE 2.11/1.60 eval_jama_ex6_bb8_in(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0) -> Com_1(eval_jama_ex6_stop(v_a, v_b, v_c, v_d, v_i.0, v_j.0, v_k.0)) :|: TRUE 2.11/1.60 2.11/1.60 The start-symbols are:[eval_jama_ex6_start_7] 2.11/1.60 2.11/1.60 2.11/1.60 ---------------------------------------- 2.11/1.60 2.11/1.60 (1) Koat Proof (FINISHED) 2.11/1.60 YES(?, 113*ar_1 + 113*ar_2 + 128*ar_1*ar_4 + 128*ar_2*ar_4 + 124*ar_1*ar_5 + 124*ar_2*ar_5 + 100*ar_4 + 96*ar_5 + 28*ar_1^2*ar_4 + 56*ar_1*ar_2*ar_4 + 28*ar_1^2*ar_5 + 56*ar_1*ar_2*ar_5 + 20*ar_1^2 + 40*ar_1*ar_2 + 28*ar_2^2*ar_4 + 28*ar_2^2*ar_5 + 20*ar_2^2 + 20*ar_1*ar_4^2 + 20*ar_2*ar_4^2 + 36*ar_1*ar_4*ar_5 + 36*ar_2*ar_4*ar_5 + 12*ar_4^2 + 20*ar_4*ar_5 + 8*ar_1^2*ar_4^2 + 16*ar_1*ar_2*ar_4^2 + 16*ar_1^2*ar_4*ar_5 + 32*ar_1*ar_2*ar_4*ar_5 + 8*ar_2^2*ar_4^2 + 16*ar_2^2*ar_4*ar_5 + 8*ar_1^2*ar_5^2 + 16*ar_1*ar_2*ar_5^2 + 16*ar_1*ar_5^2 + 8*ar_2^2*ar_5^2 + 16*ar_2*ar_5^2 + 8*ar_5^2 + 99) 2.11/1.60 2.11/1.60 2.11/1.60 2.11/1.60 Initial complexity problem: 2.11/1.60 2.11/1.60 1: T: 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_3 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_5 + 1 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 - ar_3)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 + ar_3 >= ar_6 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= ar_0 + ar_3 + 1 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6 + 1)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_3 + 1, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb1in(ar_0 + 1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6stop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ 0 <= 0 ] 2.11/1.60 2.11/1.60 start location: koat_start 2.11/1.60 2.11/1.60 leaf cost: 0 2.11/1.60 2.11/1.60 2.11/1.60 2.11/1.60 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.11/1.60 2.11/1.60 2: T: 2.11/1.60 2.11/1.60 (Comp: 1, Cost: 1) evaljamaex6start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: 1, Cost: 1) evaljamaex6bb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb1in(ar_1, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_4, ar_4, ar_5, ar_6)) [ ar_2 >= ar_0 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb8in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 >= ar_2 + 1 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_5 >= ar_3 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb7in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_3 >= ar_5 + 1 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 - ar_3)) 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb5in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_0 + ar_3 >= ar_6 ] 2.11/1.60 2.11/1.60 (Comp: ?, Cost: 1) evaljamaex6bb4in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6) -> Com_1(evaljamaex6bb6in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6)) [ ar_6 >= ar_0 + ar_3 + 1 ]
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