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TRS Stand 20472 pair #381710981
details
property
value
status
complete
benchmark
aprove1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.05259490013 seconds
cpu usage
8.579799742
max memory
5.3792768E8
stage attributes
key
value
output-size
29009
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 15 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) QDPOrderProof [EQUIVALENT, 27 ms] (29) QDP (30) UsableRulesProof [EQUIVALENT, 0 ms] (31) QDP (32) ATransformationProof [EQUIVALENT, 0 ms] (33) QDP (34) QReductionProof [EQUIVALENT, 0 ms] (35) QDP (36) TransformationProof [EQUIVALENT, 0 ms] (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) QDP (40) UsableRulesProof [EQUIVALENT, 0 ms] (41) QDP (42) QReductionProof [EQUIVALENT, 0 ms] (43) QDP (44) MRRProof [EQUIVALENT, 0 ms] (45) QDP (46) QDPOrderProof [EQUIVALENT, 0 ms] (47) QDP (48) DependencyGraphProof [EQUIVALENT, 0 ms] (49) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ap(ap(map, f), xs) -> ap(ap(ap(if, ap(isEmpty, xs)), f), xs) ap(ap(ap(if, true), f), xs) -> null ap(ap(ap(if, null), f), xs) -> ap(ap(cons, ap(f, ap(last, xs))), ap(ap(if2, f), xs)) ap(ap(if2, f), xs) -> ap(ap(map, f), ap(dropLast, xs)) ap(isEmpty, null) -> true ap(isEmpty, ap(ap(cons, x), xs)) -> null ap(last, ap(ap(cons, x), null)) -> x ap(last, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(last, ap(ap(cons, y), ys)) ap(dropLast, ap(ap(cons, x), null)) -> null ap(dropLast, ap(ap(cons, x), ap(ap(cons, y), ys))) -> ap(ap(cons, x), ap(dropLast, ap(ap(cons, y), ys))) 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: ap(ap(map, f), xs) -> ap(ap(ap(if, ap(isEmpty, xs)), f), xs) ap(ap(ap(if, true), f), xs) -> null ap(ap(ap(if, null), f), xs) -> ap(ap(cons, ap(f, ap(last, xs))), ap(ap(if2, f), xs)) ap(ap(if2, f), xs) -> ap(ap(map, f), ap(dropLast, xs))
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