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TRS Context Sensitive pair #516978937
details
property
value
status
complete
benchmark
MYNAT_nosorts-peanoSimple.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
Maude_06
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.84769296646 seconds
cpu usage
4.449220607
max memory
4.74505216E8
stage attributes
key
value
output-size
2846
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 47 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 2 ms] (6) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: and(tt, X) -> X plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) The replacement map contains the following entries: and: {1} tt: empty set plus: {1, 2} 0: empty set s: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: and(tt, X) -> X plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) The replacement map contains the following entries: and: {1} tt: empty set plus: {1, 2} 0: empty set s: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(and(x_1, x_2)) = 2*x_1 + x_2 POL(plus(x_1, x_2)) = 2*x_1 + 2*x_2 POL(s(x_1)) = x_1 POL(tt) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: and(tt, X) -> X plus(N, 0) -> N ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: plus(N, s(M)) -> s(plus(N, M)) The replacement map contains the following entries: plus: {1, 2} s: {1} ---------------------------------------- (3) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: plus(N, s(M)) -> s(plus(N, M)) The replacement map contains the following entries: plus: {1, 2} s: {1}
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