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TRS Standard pair #487072323
details
property
value
status
complete
benchmark
#3.10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
Applicative_first_order_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.87932 seconds
cpu usage
7.34508
user time
7.00528
system time
0.3398
max virtual memory
2.0143908E7
max residence set size
575696.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 24 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 137 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) QDPOrderProof [EQUIVALENT, 21 ms] (33) QDP (34) DependencyGraphProof [EQUIVALENT, 0 ms] (35) TRUE (36) QDP (37) UsableRulesProof [EQUIVALENT, 0 ms] (38) QDP (39) ATransformationProof [EQUIVALENT, 0 ms] (40) QDP (41) QReductionProof [EQUIVALENT, 0 ms] (42) QDP (43) QDPSizeChangeProof [EQUIVALENT, 0 ms] (44) YES (45) QDP (46) UsableRulesProof [EQUIVALENT, 0 ms] (47) QDP (48) ATransformationProof [EQUIVALENT, 0 ms] (49) QDP (50) QReductionProof [EQUIVALENT, 0 ms] (51) QDP (52) QDPSizeChangeProof [EQUIVALENT, 0 ms] (53) YES (54) QDP (55) UsableRulesProof [EQUIVALENT, 0 ms] (56) QDP (57) ATransformationProof [EQUIVALENT, 0 ms] (58) QDP (59) QReductionProof [EQUIVALENT, 0 ms] (60) QDP (61) QDPOrderProof [EQUIVALENT, 107 ms] (62) QDP (63) UsableRulesProof [EQUIVALENT, 0 ms] (64) QDP (65) QReductionProof [EQUIVALENT, 0 ms] (66) QDP (67) QDPSizeChangeProof [EQUIVALENT, 0 ms] (68) YES (69) QDP (70) QDPSizeChangeProof [EQUIVALENT, 0 ms] (71) 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, x)) -> false app'(app'(eq, app'(s, x)), 0) -> false app'(app'(eq, app'(s, x)), app'(s, y)) -> app'(app'(eq, x), y) app'(app'(le, 0), y) -> true app'(app'(le, app'(s, x)), 0) -> false app'(app'(le, app'(s, x)), app'(s, y)) -> app'(app'(le, x), y) app'(app'(app, nil), y) -> y app'(app'(app, app'(app'(add, n), x)), y) -> app'(app'(add, n), app'(app'(app, x), y)) app'(min, app'(app'(add, n), nil)) -> n app'(min, app'(app'(add, n), app'(app'(add, m), x))) -> app'(app'(if_min, app'(app'(le, n), m)), app'(app'(add, n), app'(app'(add, m), x))) app'(app'(if_min, true), app'(app'(add, n), app'(app'(add, m), x))) -> app'(min, app'(app'(add, n), x))
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