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TRS Standard pair #487073673
details
property
value
status
complete
benchmark
Ex9Maps.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n182.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
6.37484 seconds
cpu usage
18.1297
user time
17.2572
system time
0.872591
max virtual memory
1.8543288E7
max residence set size
2447496.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 12 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) TransformationProof [EQUIVALENT, 0 ms] (12) QDP (13) TransformationProof [EQUIVALENT, 26 ms] (14) QDP (15) TransformationProof [EQUIVALENT, 77 ms] (16) QDP (17) TransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) TransformationProof [EQUIVALENT, 237 ms] (22) QDP (23) TransformationProof [EQUIVALENT, 375 ms] (24) QDP (25) MRRProof [EQUIVALENT, 383 ms] (26) QDP (27) PisEmptyProof [EQUIVALENT, 0 ms] (28) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(map_1, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map_1, f), t)) app(app(app(map_2, f), c), app(app(cons, h), t)) -> app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t)) 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_1, f), app(app(cons, h), t)) -> app(app(cons, app(f, h)), app(app(map_1, f), t)) app(app(app(map_2, f), c), app(app(cons, h), t)) -> app(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) app(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> app(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t)) The set Q consists of the following terms: app(app(map_1, x0), app(app(cons, x1), x2)) app(app(app(map_2, x0), x1), app(app(cons, x2), x3)) app(app(app(app(map_3, x0), g), x1), app(app(cons, x2), x3)) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: APP(app(map_1, f), app(app(cons, h), t)) -> APP(app(cons, app(f, h)), app(app(map_1, f), t)) APP(app(map_1, f), app(app(cons, h), t)) -> APP(cons, app(f, h)) APP(app(map_1, f), app(app(cons, h), t)) -> APP(f, h) APP(app(map_1, f), app(app(cons, h), t)) -> APP(app(map_1, f), t) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(cons, app(app(f, h), c)), app(app(app(map_2, f), c), t)) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(cons, app(app(f, h), c)) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(f, h), c) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(f, h) APP(app(app(map_2, f), c), app(app(cons, h), t)) -> APP(app(app(map_2, f), c), t) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(app(cons, app(app(app(f, g), h), c)), app(app(app(app(map_3, f), g), c), t)) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(cons, app(app(app(f, g), h), c)) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(app(app(f, g), h), c) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(app(f, g), h) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(f, g) APP(app(app(app(map_3, f), g), c), app(app(cons, h), t)) -> APP(app(app(app(map_3, f), g), c), t)
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