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SRS Relative pair #487521276
details
property
value
status
complete
benchmark
random-227.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Waldmann_19
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.74967813492 seconds
cpu usage
11.730093337
max memory
1.331183616E9
stage attributes
key
value
output-size
4184
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 408 ms] (2) RelTRS (3) SIsEmptyProof [EQUIVALENT, 0 ms] (4) QTRS (5) RFCMatchBoundsTRSProof [EQUIVALENT, 8 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: c(b(c(x1))) -> c(a(b(x1))) c(b(b(x1))) -> a(a(c(x1))) a(a(b(x1))) -> b(b(c(x1))) b(b(c(x1))) -> a(b(c(x1))) b(b(b(x1))) -> b(a(b(x1))) The relative TRS consists of the following S rules: c(b(a(x1))) -> b(a(c(x1))) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(c(x_1)) = [[0], [2]] + [[2, 0], [0, 2]] * x_1 >>> <<< POL(b(x_1)) = [[2], [0]] + [[2, 2], [0, 0]] * x_1 >>> <<< POL(a(x_1)) = [[2], [0]] + [[2, 0], [0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: c(b(b(x1))) -> a(a(c(x1))) Rules from S: c(b(a(x1))) -> b(a(c(x1))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: c(b(c(x1))) -> c(a(b(x1))) a(a(b(x1))) -> b(b(c(x1))) b(b(c(x1))) -> a(b(c(x1))) b(b(b(x1))) -> b(a(b(x1))) S is empty. ---------------------------------------- (3) SIsEmptyProof (EQUIVALENT) The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: c(b(c(x1))) -> c(a(b(x1))) a(a(b(x1))) -> b(b(c(x1))) b(b(c(x1))) -> a(b(c(x1))) b(b(b(x1))) -> b(a(b(x1))) Q is empty.
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