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TRS Context Sensitive pair #487523845
details
property
value
status
complete
benchmark
Ex4_7_15_Bor03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n184.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.84372901917 seconds
cpu usage
3.536701105
max memory
2.0037632E8
stage attributes
key
value
output-size
2877
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 48 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f(0) -> cons(0, f(s(0))) f(s(0)) -> f(p(s(0))) p(s(0)) -> 0 The replacement map contains the following entries: f: {1} 0: empty set cons: {1} s: {1} p: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f(0) -> cons(0, f(s(0))) f(s(0)) -> f(p(s(0))) p(s(0)) -> 0 The replacement map contains the following entries: f: {1} 0: empty set cons: {1} s: {1} p: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 2 POL(cons(x_1, x_2)) = x_1 POL(f(x_1)) = 1 + 2*x_1 POL(p(x_1)) = x_1 POL(s(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(0) -> cons(0, f(s(0))) p(s(0)) -> 0 ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f(s(0)) -> f(p(s(0))) The replacement map contains the following entries: f: {1} 0: empty set s: {1} p: {1} ---------------------------------------- (3) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f(s(0)) -> f(p(s(0))) The replacement map contains the following entries:
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