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TRS Relat 75837 pair #381724879
details
property
value
status
complete
benchmark
rtL-cbn1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n094.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.72647213936 seconds
cpu usage
19.673603713
max memory
3.363987456E9
stage attributes
key
value
output-size
29498
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 70 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 55 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 33 ms] (6) RelTRS (7) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 238 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 34 ms] (10) RelTRS (11) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 88 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 0 ms] (14) RelTRS (15) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 38 ms] (16) RelTRS (17) RelTRSRRRProof [EQUIVALENT, 0 ms] (18) RelTRS (19) RIsEmptyProof [EQUIVALENT, 0 ms] (20) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: Tl(O(x), y) -> Wr(check(x), y) Tl(O(x), y) -> Wr(x, check(y)) Tl(N(x), y) -> Wr(check(x), y) Tl(N(x), y) -> Wr(x, check(y)) Tr(x, O(y)) -> Wl(check(x), y) Tr(x, O(y)) -> Wl(x, check(y)) Tr(x, N(y)) -> Wl(check(x), y) Tr(x, N(y)) -> Wl(x, check(y)) Tl(B, y) -> Wr(check(B), y) Tl(B, y) -> Wr(B, check(y)) Tr(x, B) -> Wl(check(x), B) Tr(x, B) -> Wl(x, check(B)) The relative TRS consists of the following S rules: Tl(O(x), y) -> Wl(check(x), y) Tl(O(x), y) -> Wl(x, check(y)) Tl(N(x), y) -> Wl(check(x), y) Tl(N(x), y) -> Wl(x, check(y)) Tr(x, O(y)) -> Wr(check(x), y) Tr(x, O(y)) -> Wr(x, check(y)) Tr(x, N(y)) -> Wr(check(x), y) Tr(x, N(y)) -> Wr(x, check(y)) B -> N(B) check(O(x)) -> ok(O(x)) Wl(ok(x), y) -> Tl(x, y) Wl(x, ok(y)) -> Tl(x, y) Wr(ok(x), y) -> Tr(x, y) Wr(x, ok(y)) -> Tr(x, y) check(O(x)) -> O(check(x)) check(N(x)) -> N(check(x)) O(ok(x)) -> ok(O(x)) N(ok(x)) -> ok(N(x)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(B) = 0 POL(N(x_1)) = x_1 POL(O(x_1)) = 1 + x_1 POL(Tl(x_1, x_2)) = x_1 + x_2 POL(Tr(x_1, x_2)) = x_1 + x_2 POL(Wl(x_1, x_2)) = x_1 + x_2 POL(Wr(x_1, x_2)) = x_1 + x_2 POL(check(x_1)) = x_1 POL(ok(x_1)) = x_1 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: Tl(O(x), y) -> Wr(check(x), y) Tl(O(x), y) -> Wr(x, check(y)) Tr(x, O(y)) -> Wl(check(x), y) Tr(x, O(y)) -> Wl(x, check(y))
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