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TRS Standard pair #487073308
details
property
value
status
complete
benchmark
011.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
AotoYamada_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
17.1618 seconds
cpu usage
46.2914
user time
44.3151
system time
1.97634
max virtual memory
1.8784056E7
max residence set size
4664676.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) ATransformationProof [EQUIVALENT, 0 ms] (13) QDP (14) QReductionProof [EQUIVALENT, 0 ms] (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 0 ms] (17) YES (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QReductionProof [EQUIVALENT, 0 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 0 ms] (24) QDP (25) TransformationProof [EQUIVALENT, 0 ms] (26) QDP (27) TransformationProof [EQUIVALENT, 10 ms] (28) QDP (29) QDPOrderProof [EQUIVALENT, 965 ms] (30) QDP (31) UsableRulesProof [EQUIVALENT, 0 ms] (32) QDP (33) ATransformationProof [EQUIVALENT, 0 ms] (34) QDP (35) QReductionProof [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(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) 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(app(curry, g), x), y) -> app(app(g, x), y) inc -> app(map, app(app(curry, plus), app(s, 0))) 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(plus, 0), y) -> y app(app(plus, app(s, x)), y) -> app(s, app(app(plus, x), y)) 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(app(curry, g), x), y) -> app(app(g, x), y) inc -> app(map, app(app(curry, plus), app(s, 0))) The set Q consists of the following terms: app(app(plus, 0), x0) app(app(plus, app(s, x0)), x1) app(app(map, x0), nil) app(app(map, x0), app(app(cons, x1), x2)) app(app(app(curry, x0), x1), x2) inc ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation:
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