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TRS Standard pair #516967985
details
property
value
status
complete
benchmark
cade16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
GTSSK07
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.92181897163 seconds
cpu usage
7.889744884
max memory
5.257216E8
stage attributes
key
value
output-size
18254
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 1 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 1 ms] (25) QDP (26) NonInfProof [EQUIVALENT, 23 ms] (27) QDP (28) DependencyGraphProof [EQUIVALENT, 0 ms] (29) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) 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: nthtail(n, l) -> cond(ge(n, length(l)), n, l) cond(true, n, l) -> l cond(false, n, l) -> tail(nthtail(s(n), l)) tail(nil) -> nil tail(cons(x, l)) -> l length(nil) -> 0 length(cons(x, l)) -> s(length(l)) ge(u, 0) -> true ge(0, s(v)) -> false ge(s(u), s(v)) -> ge(u, v) The set Q consists of the following terms: nthtail(x0, x1) cond(true, x0, x1) cond(false, x0, x1) tail(nil) tail(cons(x0, x1)) length(nil) length(cons(x0, x1)) ge(x0, 0) ge(0, s(x0)) ge(s(x0), s(x1))
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