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TRS Stand 20472 pair #381714472
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
n072.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
9.84321904182 seconds
cpu usage
20.519551522
max memory
1.14008064E9
stage attributes
key
value
output-size
39448
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0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, 88 ms] (34) QDP (35) NonInfProof [EQUIVALENT, 23 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} ----------------------------------------
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