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TRS Relative pair #487081914
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
n149.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.83133 seconds
cpu usage
15.6953
user time
14.761
system time
0.934292
max virtual memory
3.6446876E7
max residence set size
2562404.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 57 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 63 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 41 ms] (6) RelTRS (7) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 183 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 16 ms] (10) RelTRS (11) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 112 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 14 ms] (14) RelTRS (15) RelTRSSemanticLabellingPOLOProof [EQUIVALENT, 59 ms] (16) RelTRS (17) RelTRSRRRProof [EQUIVALENT, 5 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)) Rules from S: Tl(O(x), y) -> Wl(check(x), y) Tl(O(x), y) -> Wl(x, check(y)) Tr(x, O(y)) -> Wr(check(x), y) Tr(x, O(y)) -> Wr(x, check(y))
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