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TRS Relative pair #487081812
details
property
value
status
complete
benchmark
trafic.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Mixed_relative_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
5.63853 seconds
cpu usage
18.7419
user time
17.8256
system time
0.916284
max virtual memory
1.8744464E7
max residence set size
2281264.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 132 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 260 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 168 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 147 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 94 ms] (10) RelTRS (11) RelTRSRRRProof [EQUIVALENT, 67 ms] (12) RelTRS (13) RelTRSRRRProof [EQUIVALENT, 54 ms] (14) RelTRS (15) RelTRSRRRProof [EQUIVALENT, 66 ms] (16) RelTRS (17) RelTRSRRRProof [EQUIVALENT, 7 ms] (18) RelTRS (19) RelTRSRRRProof [EQUIVALENT, 0 ms] (20) RelTRS (21) RelTRSRRRProof [EQUIVALENT, 7 ms] (22) RelTRS (23) RIsEmptyProof [EQUIVALENT, 0 ms] (24) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: top(north(old(n), e, s, w)) -> top(east(n, e, s, w)) top(north(new(n), old(e), s, w)) -> top(east(n, old(e), s, w)) top(north(new(n), e, old(s), w)) -> top(east(n, e, old(s), w)) top(north(new(n), e, s, old(w))) -> top(east(n, e, s, old(w))) top(east(n, old(e), s, w)) -> top(south(n, e, s, w)) top(east(old(n), new(e), s, w)) -> top(south(old(n), e, s, w)) top(east(n, new(e), old(s), w)) -> top(south(n, e, old(s), w)) top(east(n, new(e), s, old(w))) -> top(south(n, e, s, old(w))) top(south(n, e, old(s), w)) -> top(west(n, e, s, w)) top(south(old(n), e, new(s), w)) -> top(west(old(n), e, s, w)) top(south(n, old(e), new(s), w)) -> top(west(n, old(e), s, w)) top(south(n, e, new(s), old(w))) -> top(west(n, e, s, old(w))) top(west(n, e, s, old(w))) -> top(north(n, e, s, w)) top(west(old(n), e, s, new(w))) -> top(north(old(n), e, s, w)) top(west(n, old(e), s, new(w))) -> top(north(n, old(e), s, w)) top(west(n, e, old(s), new(w))) -> top(north(n, e, old(s), w)) top(north(bot, old(e), s, w)) -> top(east(bot, old(e), s, w)) top(north(bot, e, old(s), w)) -> top(east(bot, e, old(s), w)) top(north(bot, e, s, old(w))) -> top(east(bot, e, s, old(w))) top(east(old(n), bot, s, w)) -> top(south(old(n), bot, s, w)) top(east(n, bot, old(s), w)) -> top(south(n, bot, old(s), w)) top(east(n, bot, s, old(w))) -> top(south(n, bot, s, old(w))) top(south(old(n), e, bot, w)) -> top(west(old(n), e, bot, w)) top(south(n, old(e), bot, w)) -> top(west(n, old(e), bot, w)) top(south(n, e, bot, old(w))) -> top(west(n, e, bot, old(w))) top(west(old(n), e, s, bot)) -> top(north(old(n), e, s, bot)) top(west(n, old(e), s, bot)) -> top(north(n, old(e), s, bot)) top(west(n, e, old(s), bot)) -> top(north(n, e, old(s), bot)) The relative TRS consists of the following S rules: top(north(old(n), e, s, w)) -> top(north(n, e, s, w)) top(north(new(n), e, s, w)) -> top(north(n, e, s, w)) top(east(n, old(e), s, w)) -> top(east(n, e, s, w)) top(east(n, new(e), s, w)) -> top(east(n, e, s, w)) top(south(n, e, old(s), w)) -> top(south(n, e, s, w)) top(south(n, e, new(s), w)) -> top(south(n, e, s, w)) top(west(n, e, s, old(w))) -> top(west(n, e, s, w)) top(west(n, e, s, new(w))) -> top(west(n, e, s, w)) bot -> new(bot) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(bot) = 0 POL(east(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(new(x_1)) = x_1 POL(north(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(old(x_1)) = 1 + x_1 POL(south(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 POL(top(x_1)) = x_1 POL(west(x_1, x_2, x_3, x_4)) = x_1 + x_2 + x_3 + x_4 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R:
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