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TRS Standard pair #487073023
details
property
value
status
complete
benchmark
otto08.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
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.73532 seconds
cpu usage
8.68035
user time
8.35856
system time
0.321792
max virtual memory
1.8552108E7
max residence set size
440868.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 0 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) TransformationProof [EQUIVALENT, 0 ms] (34) QDP (35) NonInfProof [EQUIVALENT, 0 ms] (36) AND (37) QDP (38) DependencyGraphProof [EQUIVALENT, 0 ms] (39) TRUE (40) QDP (41) DependencyGraphProof [EQUIVALENT, 0 ms] (42) TRUE ---------------------------------------- (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) minus(x, 0) -> x minus(0, s(y)) -> 0 minus(s(x), s(y)) -> minus(x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) mod(s(x), 0) -> 0 mod(x, s(y)) -> help(x, s(y), 0) help(x, s(y), c) -> if(le(c, x), x, s(y), c) if(true, x, s(y), c) -> help(x, s(y), plus(c, s(y))) if(false, x, s(y), c) -> minus(x, minus(c, s(y))) 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) minus(x, 0) -> x minus(0, s(y)) -> 0 minus(s(x), s(y)) -> minus(x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) mod(s(x), 0) -> 0 mod(x, s(y)) -> help(x, s(y), 0) help(x, s(y), c) -> if(le(c, x), x, s(y), c) if(true, x, s(y), c) -> help(x, s(y), plus(c, s(y))) if(false, x, s(y), c) -> minus(x, minus(c, s(y)))
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