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Complexity_C_Integer 2019-03-21 04.38 pair #429988958
details
property
value
status
complete
benchmark
LeikeHeizmann-TACAS2014-Ex9_true-termination.c
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n173.star.cs.uiowa.edu
space
Adapted_from_Stroeder_15
run statistics
property
value
solver
AProVE
configuration
c_complexity
runtime (wallclock)
1.72654 seconds
cpu usage
2.55148
user time
2.33608
system time
0.215396
max virtual memory
1.833918E7
max residence set size
183188.0
stage attributes
key
value
starexec-result
WORST_CASE(?, O(n^1))
output
2.07/1.67 WORST_CASE(?, O(n^1)) 2.07/1.68 proof of /export/starexec/sandbox2/output/output_files/bench.koat 2.07/1.68 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 2.07/1.68 2.07/1.68 2.07/1.68 The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). 2.07/1.68 2.07/1.68 (0) CpxIntTrs 2.07/1.68 (1) Koat Proof [FINISHED, 361 ms] 2.07/1.68 (2) BOUNDS(1, n^1) 2.07/1.68 2.07/1.68 2.07/1.68 ---------------------------------------- 2.07/1.68 2.07/1.68 (0) 2.07/1.68 Obligation: 2.07/1.68 Complexity Int TRS consisting of the following rules: 2.07/1.68 eval_foo_start(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_p, v_q)) :|: TRUE 2.07/1.68 eval_foo_bb0_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_p, v_q, v_p, v_q)) :|: TRUE 2.07/1.68 eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 > 0 && v_.0 > 0 && v_.0 < v_.01 2.07/1.68 eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 > 0 && v_.0 > 0 && v_.0 > v_.01 2.07/1.68 eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 <= 0 2.07/1.68 eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 <= 0 2.07/1.68 eval_foo_bb1_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 >= v_.01 && v_.0 <= v_.01 2.07/1.68 eval_foo_bb2_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 < v_.0 2.07/1.68 eval_foo_bb2_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb4_in(v_.0, v_.01, v_p, v_q)) :|: v_.01 >= v_.0 2.07/1.68 eval_foo_bb3_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0, v_.01 - 1, v_p, v_q)) :|: TRUE 2.07/1.68 eval_foo_bb4_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0 - 1, v_.01, v_p, v_q)) :|: v_.0 < v_.01 2.07/1.68 eval_foo_bb4_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_bb1_in(v_.0, v_.01, v_p, v_q)) :|: v_.0 >= v_.01 2.07/1.68 eval_foo_.critedge_in(v_.0, v_.01, v_p, v_q) -> Com_1(eval_foo_stop(v_.0, v_.01, v_p, v_q)) :|: TRUE 2.07/1.68 2.07/1.68 The start-symbols are:[eval_foo_start_4] 2.07/1.68 2.07/1.68 2.07/1.68 ---------------------------------------- 2.07/1.68 2.07/1.68 (1) Koat Proof (FINISHED) 2.07/1.68 YES(?, 7*ar_1 + 14*ar_3 + 14) 2.07/1.68 2.07/1.68 2.07/1.68 2.07/1.68 Initial complexity problem: 2.07/1.68 2.07/1.68 1: T: 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb3in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2 - 1, ar_3)) 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0 - 1, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb4in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoocritedgein(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostop(ar_0, ar_1, ar_2, ar_3)) 2.07/1.68 2.07/1.68 (Comp: 1, Cost: 0) koat_start(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoostart(ar_0, ar_1, ar_2, ar_3)) [ 0 <= 0 ] 2.07/1.68 2.07/1.68 start location: koat_start 2.07/1.68 2.07/1.68 leaf cost: 0 2.07/1.68 2.07/1.68 2.07/1.68 2.07/1.68 Repeatedly propagating knowledge in problem 1 produces the following problem: 2.07/1.68 2.07/1.68 2: T: 2.07/1.68 2.07/1.68 (Comp: 1, Cost: 1) evalfoostart(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb0in(ar_0, ar_1, ar_2, ar_3)) 2.07/1.68 2.07/1.68 (Comp: 1, Cost: 1) evalfoobb0in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb1in(ar_1, ar_1, ar_3, ar_3)) 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_2 >= ar_0 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb2in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= 1 /\ ar_0 >= 1 /\ ar_0 >= ar_2 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_2 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ 0 >= ar_0 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb1in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoocritedgein(ar_0, ar_1, ar_2, ar_3)) [ ar_0 = ar_2 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb3in(ar_0, ar_1, ar_2, ar_3)) [ ar_0 >= ar_2 + 1 ] 2.07/1.68 2.07/1.68 (Comp: ?, Cost: 1) evalfoobb2in(ar_0, ar_1, ar_2, ar_3) -> Com_1(evalfoobb4in(ar_0, ar_1, ar_2, ar_3)) [ ar_2 >= ar_0 ]
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