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TRS Inner 89993 pair #381733493
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
n041.star.cs.uiowa.edu
space
Applicative_AG01_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.6536231041 seconds
cpu usage
7.012095842
max memory
4.93621248E8
stage attributes
key
value
output-size
61371
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 94 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) ATransformationProof [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) ATransformationProof [EQUIVALENT, 0 ms] (18) QDP (19) QReductionProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 26 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE (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) ATransformationProof [EQUIVALENT, 0 ms] (38) QDP (39) QReductionProof [EQUIVALENT, 0 ms] (40) QDP (41) QDPSizeChangeProof [EQUIVALENT, 0 ms] (42) YES (43) QDP (44) UsableRulesProof [EQUIVALENT, 0 ms] (45) QDP (46) ATransformationProof [EQUIVALENT, 0 ms] (47) QDP (48) QReductionProof [EQUIVALENT, 0 ms] (49) QDP (50) QDPOrderProof [EQUIVALENT, 76 ms] (51) QDP (52) PisEmptyProof [EQUIVALENT, 0 ms] (53) YES (54) QDP (55) QDPSizeChangeProof [EQUIVALENT, 0 ms] (56) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: app(app(eq, 0), 0) -> true app(app(eq, 0), app(s, m)) -> false app(app(eq, app(s, n)), 0) -> false app(app(eq, app(s, n)), app(s, m)) -> app(app(eq, n), m) app(app(le, 0), m) -> true app(app(le, app(s, n)), 0) -> false app(app(le, app(s, n)), app(s, m)) -> app(app(le, n), m) app(min, app(app(cons, 0), nil)) -> 0 app(min, app(app(cons, app(s, n)), nil)) -> app(s, n) app(min, app(app(cons, n), app(app(cons, m), x))) -> app(app(if_min, app(app(le, n), m)), app(app(cons, n), app(app(cons, m), x))) app(app(if_min, true), app(app(cons, n), app(app(cons, m), x))) -> app(min, app(app(cons, n), x)) app(app(if_min, false), app(app(cons, n), app(app(cons, m), x))) -> app(min, app(app(cons, m), x)) app(app(app(replace, n), m), nil) -> nil app(app(app(replace, n), m), app(app(cons, k), x)) -> app(app(app(app(if_replace, app(app(eq, n), k)), n), m), app(app(cons, k), x)) app(app(app(app(if_replace, true), n), m), app(app(cons, k), x)) -> app(app(cons, m), x) app(app(app(app(if_replace, false), n), m), app(app(cons, k), x)) -> app(app(cons, k), app(app(app(replace, n), m), x)) app(sort, nil) -> nil app(sort, app(app(cons, n), x)) -> app(app(cons, app(min, app(app(cons, n), x))), app(sort, app(app(app(replace, app(min, app(app(cons, n), x))), n), x))) 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(filter, f), nil) -> nil
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