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TRS Context Sensitive pair #487523823
details
property
value
status
complete
benchmark
Ex6_Luc98.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)
1.6284570694 seconds
cpu usage
3.496502932
max memory
2.0299776E8
stage attributes
key
value
output-size
3957
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 41 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 3 ms] (6) CSR (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: first: {1, 2} 0: empty set nil: empty set s: {1} cons: {1} from: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: first: {1, 2} 0: empty set nil: empty set s: {1} cons: {1} from: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(cons(x_1, x_2)) = 1 + x_1 POL(first(x_1, x_2)) = 1 + x_1 + x_2 POL(from(x_1)) = 1 + x_1 POL(nil) = 1 POL(s(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: first(0, X) -> nil from(X) -> cons(X, from(s(X))) The replacement map contains the following entries: first: {1, 2} 0: empty set nil: empty set s: {1} cons: {1} from: {1} ---------------------------------------- (3) CSRRRRProof (EQUIVALENT)
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