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TRS Context Sensitive pair #487523817
details
property
value
status
complete
benchmark
Ex1_Luc04b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n022.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.51946306229 seconds
cpu usage
3.477571826
max memory
2.1352448E8
stage attributes
key
value
output-size
7053
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 45 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 6 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: nats -> cons(0, incr(nats)) pairs -> cons(0, incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), incr(XS)) head(cons(X, XS)) -> X tail(cons(X, XS)) -> XS The replacement map contains the following entries: nats: empty set cons: {1} 0: empty set incr: {1} pairs: empty set odds: empty set s: {1} head: {1} tail: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: nats -> cons(0, incr(nats)) pairs -> cons(0, incr(odds)) odds -> incr(pairs) incr(cons(X, XS)) -> cons(s(X), incr(XS)) head(cons(X, XS)) -> X tail(cons(X, XS)) -> XS The replacement map contains the following entries: nats: empty set cons: {1} 0: empty set incr: {1} pairs: empty set odds: empty set s: {1} head: {1} tail: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(cons(x_1, x_2)) = x_1 + x_2 POL(head(x_1)) = 1 + x_1 POL(incr(x_1)) = x_1 POL(nats) = 0 POL(odds) = 0 POL(pairs) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: head(cons(X, XS)) -> X ---------------------------------------- (2)
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