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TRS Relative pair #487520763
details
property
value
status
complete
benchmark
rt3-2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.89695620537 seconds
cpu usage
4.704086318
max memory
3.36297984E8
stage attributes
key
value
output-size
2410
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 31 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 12 ms] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: p(0, y) -> y p(s(x), y) -> s(p(x, y)) The relative TRS consists of the following S rules: p(x, y) -> p(x, s(y)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(0) = 0 POL(p(x_1, x_2)) = 1 + x_1 + x_2 POL(s(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: p(0, y) -> y Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: p(s(x), y) -> s(p(x, y)) The relative TRS consists of the following S rules: p(x, y) -> p(x, s(y)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(p(x_1, x_2)) = [[0], [0]] + [[1, 1], [1, 1]] * x_1 + [[1, 0], [1, 0]] * x_2 >>> <<< POL(s(x_1)) = [[0], [1]] + [[1, 0], [0, 1]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: p(s(x), y) -> s(p(x, y)) Rules from S: none ---------------------------------------- (4) Obligation: Relative term rewrite system: R is empty.
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