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TRS Standard pair #487072283
details
property
value
status
complete
benchmark
aprove05.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n192.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.82521 seconds
cpu usage
7.27817
user time
6.96907
system time
0.309107
max virtual memory
1.86779E7
max residence set size
467552.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 8 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) NonInfProof [EQUIVALENT, 11 ms] (27) AND (28) QDP (29) DependencyGraphProof [EQUIVALENT, 0 ms] (30) TRUE (31) QDP (32) DependencyGraphProof [EQUIVALENT, 0 ms] (33) TRUE (34) QDP (35) UsableRulesProof [EQUIVALENT, 0 ms] (36) QDP (37) QReductionProof [EQUIVALENT, 0 ms] (38) QDP (39) QDPOrderProof [EQUIVALENT, 84 ms] (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: prod(xs) -> prodIter(xs, s(0)) prodIter(xs, x) -> ifProd(isempty(xs), xs, x) ifProd(true, xs, x) -> x ifProd(false, xs, x) -> prodIter(tail(xs), times(x, head(xs))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0, 0) timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u) ifTimes(true, x, y, z, u) -> z ifTimes(false, x, y, z, u) -> timesIter(x, y, plus(y, z), s(u)) isempty(nil) -> true isempty(cons(x, xs)) -> false head(nil) -> error head(cons(x, xs)) -> x tail(nil) -> nil tail(cons(x, xs)) -> xs ge(x, 0) -> true ge(0, s(y)) -> false ge(s(x), s(y)) -> ge(x, y) a -> b a -> c Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is ifProd(true, xs, x) -> x ifProd(false, xs, x) -> prodIter(tail(xs), times(x, head(xs))) plus(0, y) -> y plus(s(x), y) -> s(plus(x, y)) times(x, y) -> timesIter(x, y, 0, 0) timesIter(x, y, z, u) -> ifTimes(ge(u, x), x, y, z, u) ifTimes(true, x, y, z, u) -> z ifTimes(false, x, y, z, u) -> timesIter(x, y, plus(y, z), s(u)) isempty(nil) -> true isempty(cons(x, xs)) -> false head(nil) -> error head(cons(x, xs)) -> x tail(nil) -> nil
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