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TRS Standard pair #487069288
details
property
value
status
complete
benchmark
quick.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n177.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.13714 seconds
cpu usage
5.13078
user time
4.87047
system time
0.260311
max virtual memory
1.9210756E7
max residence set size
378204.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 20 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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPSizeChangeProof [EQUIVALENT, 0 ms] (20) YES (21) QDP (22) UsableRulesProof [EQUIVALENT, 0 ms] (23) QDP (24) QReductionProof [EQUIVALENT, 0 ms] (25) QDP (26) QDPSizeChangeProof [EQUIVALENT, 0 ms] (27) YES (28) QDP (29) UsableRulesProof [EQUIVALENT, 0 ms] (30) QDP (31) QReductionProof [EQUIVALENT, 0 ms] (32) QDP (33) QDPSizeChangeProof [EQUIVALENT, 0 ms] (34) YES (35) QDP (36) UsableRulesProof [EQUIVALENT, 0 ms] (37) QDP (38) QReductionProof [EQUIVALENT, 0 ms] (39) QDP (40) QDPOrderProof [EQUIVALENT, 54 ms] (41) QDP (42) PisEmptyProof [EQUIVALENT, 0 ms] (43) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) app(nil, Y) -> Y app(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L)) ifhigh(true, N, cons(M, L)) -> high(N, L) ifhigh(false, N, cons(M, L)) -> cons(M, high(N, L)) quicksort(nil) -> nil quicksort(cons(N, L)) -> app(quicksort(low(N, L)), cons(N, quicksort(high(N, L)))) 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: le(0, Y) -> true le(s(X), 0) -> false le(s(X), s(Y)) -> le(X, Y) app(nil, Y) -> Y app(cons(N, L), Y) -> cons(N, app(L, Y)) low(N, nil) -> nil low(N, cons(M, L)) -> iflow(le(M, N), N, cons(M, L)) iflow(true, N, cons(M, L)) -> cons(M, low(N, L)) iflow(false, N, cons(M, L)) -> low(N, L) high(N, nil) -> nil high(N, cons(M, L)) -> ifhigh(le(M, N), N, cons(M, L))
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