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Complexity_C_Integer 2019-03-21 04.38 pair #429989210
details
property
value
status
complete
benchmark
PodelskiRybalchenko-VMCAI2004-Ex1_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
2.37593 seconds
cpu usage
3.36271
user time
3.09629
system time
0.266412
max virtual memory
1.8533184E7
max residence set size
196112.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
3.23/2.34 WORST_CASE(?, O(n^1)) 3.23/2.35 proof of /export/starexec/sandbox2/output/output_files/bench.koat 3.23/2.35 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.23/2.35 3.23/2.35 3.23/2.35 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 3.23/2.35 3.23/2.35 (0) CpxIntTrs 3.23/2.35 (1) Koat Proof [FINISHED, 1084 ms] 3.23/2.35 (2) BOUNDS(1, n^1) 3.23/2.35 3.23/2.35 3.23/2.35 ---------------------------------------- 3.23/2.35 3.23/2.35 (0) 3.23/2.35 Obligation: 3.23/2.35 Complexity Int TRS consisting of the following rules: 3.23/2.35 eval_foo_start(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 eval_foo_bb0_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb1_in(v_i, v_j, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 eval_foo_bb1_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_.0 - v_.01 >= 1 3.23/2.35 eval_foo_bb1_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_.0 - v_.01 < 1 3.23/2.35 eval_foo_bb2_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_2(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 eval_foo_2(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos), eval_foo_3(v_.0, v_.01, nondef.0, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 eval_foo_3(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_6(v_.0, v_.01, v_2, v_.0 + v_2, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_2 < 0 3.23/2.35 eval_foo_3(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_6(v_.0, v_.01, v_2, v_.0 - v_2, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_2 >= 0 3.23/2.35 eval_foo_6(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos), eval_foo_7(v_.0, v_.01, v_2, v_5, nondef.1, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 eval_foo_7(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb1_in(v_5, v_.01 - v_6 + 1, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_6 < 0 3.23/2.35 eval_foo_7(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_bb1_in(v_5, v_.01 + v_6 + 1, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: v_6 >= 0 3.23/2.35 eval_foo_bb3_in(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos) -> Com_1(eval_foo_stop(v_.0, v_.01, v_2, v_5, v_6, v_i, v_j, v_nondetNat, v_nondetPos)) :|: TRUE 3.23/2.35 3.23/2.35 The start-symbols are:[eval_foo_start_9] 3.23/2.35 3.23/2.35 3.23/2.35 ---------------------------------------- 3.23/2.35 3.23/2.35 (1) Koat Proof (FINISHED) 3.23/2.35 YES(?, 120*ar_1 + 120*ar_3 + 6) 3.23/2.35 3.23/2.35 3.23/2.35 3.23/2.35 Initial complexity problem: 3.23/2.35 3.23/2.35 1: T: 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_0 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_5, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7), evalfoo21(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 + ar_4, ar_7)) [ 0 >= ar_4 + 1 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo3(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_0 - ar_4, ar_7)) [ ar_4 >= 0 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo60(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo61(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_5)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo6(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_2(evalfoo60(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7), evalfoo61(ar_0, ar_1, ar_2, ar_3, ar_4, i, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_6, ar_1, ar_2 - ar_7 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 >= ar_7 + 1 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo7(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_6, ar_1, ar_2 + ar_7 + 1, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_7 >= 0 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ 0 <= 0 ] 3.23/2.35 3.23/2.35 start location: koat_start 3.23/2.35 3.23/2.35 leaf cost: 0 3.23/2.35 3.23/2.35 3.23/2.35 3.23/2.35 Repeatedly propagating knowledge in problem 1 produces the following problem: 3.23/2.35 3.23/2.35 2: T: 3.23/2.35 3.23/2.35 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_0 >= ar_2 + 1 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) [ ar_2 >= ar_0 ] 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalfoo2(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35 3.23/2.35 (Comp: ?, Cost: 1) evalfoo20(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7) -> Com_1(evalVERIFIERnondetintstart(ar_0, ar_1, ar_2, ar_3, ar_4, ar_5, ar_6, ar_7)) 3.23/2.35
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