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TRS Context Sensitive pair #516978825
details
property
value
status
complete
benchmark
Ex1_GL02a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n086.star.cs.uiowa.edu
space
CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
1.90019488335 seconds
cpu usage
5.215511332
max memory
4.73837568E8
stage attributes
key
value
output-size
4511
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 76 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(s(X), s(Y)) -> eq(X, Y) eq(X, Y) -> false inf(X) -> cons(X, inf(s(X))) take(0, X) -> nil take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) length(nil) -> 0 length(cons(X, L)) -> s(length(L)) The replacement map contains the following entries: eq: empty set 0: empty set true: empty set s: empty set false: empty set inf: {1} cons: empty set take: {1, 2} nil: empty set length: {1} ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: eq(0, 0) -> true eq(s(X), s(Y)) -> eq(X, Y) eq(X, Y) -> false inf(X) -> cons(X, inf(s(X))) take(0, X) -> nil take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) length(nil) -> 0 length(cons(X, L)) -> s(length(L)) The replacement map contains the following entries: eq: empty set 0: empty set true: empty set s: empty set false: empty set inf: {1} cons: empty set take: {1, 2} nil: empty set length: {1} Used ordering: Polynomial interpretation [POLO]: POL(0) = 1 POL(cons(x_1, x_2)) = 1 + x_1 POL(eq(x_1, x_2)) = 0 POL(false) = 0 POL(inf(x_1)) = 2 + x_1 POL(length(x_1)) = 2 + x_1 POL(nil) = 1 POL(s(x_1)) = 0 POL(take(x_1, x_2)) = 2*x_1 + 2*x_2 POL(true) = 0 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: inf(X) -> cons(X, inf(s(X))) take(0, X) -> nil take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) length(nil) -> 0 length(cons(X, L)) -> s(length(L))
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