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SRS Relative pair #487521561
details
property
value
status
complete
benchmark
random-151.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n090.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
15.0193450451 seconds
cpu usage
55.640430583
max memory
4.797923328E9
stage attributes
key
value
output-size
9115
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 38 ms] (2) RelTRS (3) SIsEmptyProof [EQUIVALENT, 0 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 1 ms] (8) AND (9) QDP (10) UsableRulesProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPOrderProof [EQUIVALENT, 16 ms] (13) QDP (14) QDPOrderProof [EQUIVALENT, 215 ms] (15) QDP (16) DependencyGraphProof [EQUIVALENT, 0 ms] (17) TRUE (18) QDP (19) UsableRulesProof [EQUIVALENT, 0 ms] (20) QDP (21) QDPOrderProof [EQUIVALENT, 0 ms] (22) QDP (23) PisEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: c(b(a(x1))) -> c(b(b(x1))) b(a(c(x1))) -> b(b(c(x1))) c(c(c(x1))) -> b(c(c(x1))) a(c(a(x1))) -> b(c(b(x1))) b(c(b(x1))) -> c(b(c(x1))) a(c(b(x1))) -> b(a(c(x1))) The relative TRS consists of the following S rules: b(b(a(x1))) -> c(b(b(x1))) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(a(x_1)) = 1 + x_1 POL(b(x_1)) = x_1 POL(c(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: c(b(a(x1))) -> c(b(b(x1))) b(a(c(x1))) -> b(b(c(x1))) a(c(a(x1))) -> b(c(b(x1))) Rules from S: b(b(a(x1))) -> c(b(b(x1))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: c(c(c(x1))) -> b(c(c(x1))) b(c(b(x1))) -> c(b(c(x1))) a(c(b(x1))) -> b(a(c(x1))) S is empty. ---------------------------------------- (3) SIsEmptyProof (EQUIVALENT) The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. ----------------------------------------
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