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TRS Standard pair #487072633
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.33439 seconds
cpu usage
5.59816
user time
5.36732
system time
0.23084
max virtual memory
1.8477524E7
max residence set size
348648.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 2 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPOrderProof [EQUIVALENT, 80 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: cond1(true, x) -> cond2(even(x), x) cond2(true, x) -> cond1(neq(x, 0), div2(x)) cond2(false, x) -> cond1(neq(x, 0), p(x)) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) div2(0) -> 0 div2(s(0)) -> 0 div2(s(s(x))) -> s(div2(x)) p(0) -> 0 p(s(x)) -> x Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) div2(0) -> 0 div2(s(0)) -> 0 div2(s(s(x))) -> s(div2(x)) p(0) -> 0 p(s(x)) -> x The TRS R 2 is cond1(true, x) -> cond2(even(x), x) cond2(true, x) -> cond1(neq(x, 0), div2(x)) cond2(false, x) -> cond1(neq(x, 0), p(x)) The signature Sigma is {cond1_2, cond2_2} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: cond1(true, x) -> cond2(even(x), x) cond2(true, x) -> cond1(neq(x, 0), div2(x)) cond2(false, x) -> cond1(neq(x, 0), p(x)) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true
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