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TRS Contextsensitive pair #487092525
details
property
value
status
complete
benchmark
ExIntrod_GM01.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
CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.50803 seconds
cpu usage
3.68421
user time
3.52222
system time
0.161985
max virtual memory
1.8472856E7
max residence set size
240252.0
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 42 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSRRRRProof [EQUIVALENT, 0 ms] (8) CSR (9) CSRRRRProof [EQUIVALENT, 0 ms] (10) CSR (11) CSRRRRProof [EQUIVALENT, 0 ms] (12) CSR (13) RisEmptyProof [EQUIVALENT, 3 ms] (14) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) nats -> adx(zeros) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L The replacement map contains the following entries: incr: {1} nil: empty set cons: {1} s: {1} adx: {1} nats: empty set zeros: empty set 0: empty set head: {1} tail: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: incr(nil) -> nil incr(cons(X, L)) -> cons(s(X), incr(L)) adx(nil) -> nil adx(cons(X, L)) -> incr(cons(X, adx(L))) nats -> adx(zeros) zeros -> cons(0, zeros) head(cons(X, L)) -> X tail(cons(X, L)) -> L The replacement map contains the following entries: incr: {1} nil: empty set cons: {1} s: {1} adx: {1} nats: empty set zeros: empty set 0: empty set head: {1} tail: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 0 POL(adx(x_1)) = x_1 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) = 1 POL(nil) = 0 POL(s(x_1)) = x_1 POL(tail(x_1)) = x_1 POL(zeros) = 1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: head(cons(X, L)) -> X
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