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TRS Standard pair #487073278
details
property
value
status
complete
benchmark
otto13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n185.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
7.34468 seconds
cpu usage
20.665
user time
19.4132
system time
1.25179
max virtual memory
2.1008204E7
max residence set size
2601688.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0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) NonInfProof [EQUIVALENT, 36 ms] (34) QDP (35) NonInfProof [EQUIVALENT, 0 ms] (36) QDP (37) PisEmptyProof [EQUIVALENT, 0 ms] (38) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: le(0, y, z) -> greater(y, z) le(s(x), 0, z) -> false le(s(x), s(y), 0) -> false le(s(x), s(y), s(z)) -> le(x, y, z) greater(x, 0) -> first greater(0, s(y)) -> second greater(s(x), s(y)) -> greater(x, y) double(0) -> 0 double(s(x)) -> s(s(double(x))) triple(x) -> if(le(x, x, double(x)), x, 0, 0) if(false, x, y, z) -> true if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is double(0) -> 0 double(s(x)) -> s(s(double(x))) le(0, y, z) -> greater(y, z) le(s(x), 0, z) -> false le(s(x), s(y), 0) -> false le(s(x), s(y), s(z)) -> le(x, y, z) greater(x, 0) -> first greater(0, s(y)) -> second greater(s(x), s(y)) -> greater(x, y) The TRS R 2 is triple(x) -> if(le(x, x, double(x)), x, 0, 0) if(false, x, y, z) -> true if(first, x, y, z) -> if(le(s(x), y, s(z)), s(x), y, s(z)) if(second, x, y, z) -> if(le(s(x), s(y), z), s(x), s(y), z) The signature Sigma is {triple_1, if_4, true} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: le(0, y, z) -> greater(y, z)
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