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TRS Standard pair #516968020
details
property
value
status
complete
benchmark
cade10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n069.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.90034103394 seconds
cpu usage
7.734421314
max memory
5.29461248E8
stage attributes
key
value
output-size
13840
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms]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, 0 ms] (27) QDP (28) PisEmptyProof [EQUIVALENT, 0 ms] (29) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) trunc(0) -> 0 trunc(s(0)) -> 0 trunc(s(s(x))) -> s(s(trunc(x))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is trunc(0) -> 0 trunc(s(0)) -> 0 trunc(s(s(x))) -> s(s(trunc(x))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) The TRS R 2 is f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) The signature Sigma is {f_3} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(true, x, y) -> f(gt(x, y), trunc(x), s(y)) trunc(0) -> 0 trunc(s(0)) -> 0 trunc(s(s(x))) -> s(s(trunc(x))) gt(0, v) -> false gt(s(u), 0) -> true gt(s(u), s(v)) -> gt(u, v) The set Q consists of the following terms: f(true, x0, x1) trunc(0) trunc(s(0)) trunc(s(s(x0))) gt(0, x0) gt(s(x0), 0)
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