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TRS Stand 20472 pair #381710812
details
property
value
status
complete
benchmark
#4.36.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n109.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.22490715981 seconds
cpu usage
5.790908773
max memory
4.27302912E8
stage attributes
key
value
output-size
31806
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 24 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) QDPOrderProof [EQUIVALENT, 24 ms] (20) QDP (21) DependencyGraphProof [EQUIVALENT, 0 ms] (22) TRUE (23) QDP (24) UsableRulesProof [EQUIVALENT, 0 ms] (25) QDP (26) QReductionProof [EQUIVALENT, 0 ms] (27) QDP (28) QDPSizeChangeProof [EQUIVALENT, 0 ms] (29) YES (30) QDP (31) UsableRulesProof [EQUIVALENT, 0 ms] (32) QDP (33) QReductionProof [EQUIVALENT, 0 ms] (34) QDP (35) QDPSizeChangeProof [EQUIVALENT, 0 ms] (36) YES (37) QDP (38) UsableRulesProof [EQUIVALENT, 0 ms] (39) QDP (40) QReductionProof [EQUIVALENT, 0 ms] (41) QDP (42) QDPOrderProof [EQUIVALENT, 161 ms] (43) QDP (44) PisEmptyProof [EQUIVALENT, 0 ms] (45) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(m)) -> false eq(s(n), 0) -> false eq(s(n), s(m)) -> eq(n, m) le(0, m) -> true le(s(n), 0) -> false le(s(n), s(m)) -> le(n, m) min(cons(0, nil)) -> 0 min(cons(s(n), nil)) -> s(n) min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x))) if_min(true, cons(n, cons(m, x))) -> min(cons(n, x)) if_min(false, cons(n, cons(m, x))) -> min(cons(m, x)) replace(n, m, nil) -> nil replace(n, m, cons(k, x)) -> if_replace(eq(n, k), n, m, cons(k, x)) if_replace(true, n, m, cons(k, x)) -> cons(m, x) if_replace(false, n, m, cons(k, x)) -> cons(k, replace(n, m, x)) sort(nil) -> nil sort(cons(n, x)) -> cons(min(cons(n, x)), sort(replace(min(cons(n, x)), n, x))) 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:
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