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TRS Standard pair #487069193
details
property
value
status
complete
benchmark
cade14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.1647 seconds
cpu usage
10.7063
user time
10.3739
system time
0.332317
max virtual memory
1.8503788E7
max residence set size
532548.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 17 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 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) NonInfProof [EQUIVALENT, 1126 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: diff(x, y) -> cond1(equal(x, y), x, y) cond1(true, x, y) -> 0 cond1(false, x, y) -> cond2(gt(x, y), x, y) cond2(true, x, y) -> s(diff(x, s(y))) cond2(false, x, y) -> s(diff(s(x), y)) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: diff(x, y) -> cond1(equal(x, y), x, y) cond1(true, x, y) -> 0 cond1(false, x, y) -> cond2(gt(x, y), x, y) cond2(true, x, y) -> s(diff(x, s(y))) cond2(false, x, y) -> s(diff(s(x), y)) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) equal(0, 0) -> true equal(s(x), 0) -> false equal(0, s(y)) -> false equal(s(x), s(y)) -> equal(x, y) The set Q consists of the following terms: diff(x0, x1) cond1(true, x0, x1) cond1(false, x0, x1) cond2(true, x0, x1) cond2(false, x0, x1) gt(0, x0) gt(s(x0), 0) gt(s(x0), s(x1)) equal(0, 0) equal(s(x0), 0) equal(0, s(x0)) equal(s(x0), s(x1))
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