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TRS Stand 20472 pair #381709789
details
property
value
status
complete
benchmark
TreeLevels.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.89194989204 seconds
cpu usage
4.619545925
max memory
2.84151808E8
stage attributes
key
value
output-size
25389
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 51 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) ATransformationProof [EQUIVALENT, 0 ms] (11) QDP (12) QReductionProof [EQUIVALENT, 0 ms] (13) QDP (14) QDPSizeChangeProof [EQUIVALENT, 0 ms] (15) YES (16) QDP (17) UsableRulesProof [EQUIVALENT, 0 ms] (18) QDP (19) ATransformationProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) QDPSizeChangeProof [EQUIVALENT, 0 ms] (24) YES (25) QDP (26) UsableRulesProof [EQUIVALENT, 0 ms] (27) QDP (28) ATransformationProof [EQUIVALENT, 0 ms] (29) QDP (30) QReductionProof [EQUIVALENT, 0 ms] (31) QDP (32) QDPSizeChangeProof [EQUIVALENT, 0 ms] (33) YES (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QDPSizeChangeProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(append, xs), nil) -> xs app(app(append, nil), ys) -> ys app(app(append, app(app(cons, x), xs)), ys) -> app(app(cons, x), app(app(append, xs), ys)) app(app(zip, nil), yss) -> yss app(app(zip, xss), nil) -> xss app(app(zip, app(app(cons, xs), xss)), app(app(cons, ys), yss)) -> app(app(cons, app(app(append, xs), ys)), app(app(zip, xss), yss)) app(app(combine, xs), nil) -> xs app(app(combine, xs), app(app(cons, ys), yss)) -> app(app(combine, app(app(zip, xs), ys)), yss) app(levels, app(app(node, x), xs)) -> app(app(cons, app(app(cons, x), nil)), app(app(combine, nil), app(app(map, levels), xs))) 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: app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(append, xs), nil) -> xs app(app(append, nil), ys) -> ys app(app(append, app(app(cons, x), xs)), ys) -> app(app(cons, x), app(app(append, xs), ys)) app(app(zip, nil), yss) -> yss app(app(zip, xss), nil) -> xss app(app(zip, app(app(cons, xs), xss)), app(app(cons, ys), yss)) -> app(app(cons, app(app(append, xs), ys)), app(app(zip, xss), yss)) app(app(combine, xs), nil) -> xs app(app(combine, xs), app(app(cons, ys), yss)) -> app(app(combine, app(app(zip, xs), ys)), yss) app(levels, app(app(node, x), xs)) -> app(app(cons, app(app(cons, x), nil)), app(app(combine, nil), app(app(map, levels), xs))) The set Q consists of the following terms:
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