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TRS Relative pair #487081887
details
property
value
status
complete
benchmark
rtL-me3.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
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.35609 seconds
cpu usage
6.13737
user time
5.85604
system time
0.281329
max virtual memory
1.8610652E7
max residence set size
551776.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS S Cleaner [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 74 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 4 ms] (10) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: topB(i, N1(x), y) -> topA(1, T1(x), y) topA(i, x, N2(y)) -> topB(0, x, T2(y)) topB(i, S1(x), y) -> topA(i, N1(x), y) topA(i, x, S2(y)) -> topB(i, x, N2(y)) topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y)) topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y)) The relative TRS consists of the following S rules: topA(i, N1(x), y) -> topA(1, T1(x), y) topB(i, x, N2(y)) -> topB(0, x, T2(y)) topA(i, S1(x), y) -> topA(i, N1(x), y) topB(i, x, S2(y)) -> topB(i, x, N2(y)) topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y)) topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y)) topA(i, N1(x), y) -> topA(i, N1(C(x)), y) topB(i, x, N2(y)) -> topB(i, x, N2(C(y))) topA(i, T1(x), y) -> topA(i, T1(x), y) topB(i, x, T2(y)) -> topB(i, x, T2(y)) topB(i, x, S2(y)) -> topB(i, x, S2(D(y))) ---------------------------------------- (1) RelTRS S Cleaner (EQUIVALENT) We have deleted all rules from S that have the shape t -> t: topA(i, T1(x), y) -> topA(i, T1(x), y) topB(i, x, T2(y)) -> topB(i, x, T2(y)) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: topB(i, N1(x), y) -> topA(1, T1(x), y) topA(i, x, N2(y)) -> topB(0, x, T2(y)) topB(i, S1(x), y) -> topA(i, N1(x), y) topA(i, x, S2(y)) -> topB(i, x, N2(y)) topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y)) topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y)) The relative TRS consists of the following S rules: topA(i, N1(x), y) -> topA(1, T1(x), y) topB(i, x, N2(y)) -> topB(0, x, T2(y)) topA(i, S1(x), y) -> topA(i, N1(x), y) topB(i, x, S2(y)) -> topB(i, x, N2(y)) topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y)) topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y)) topA(i, N1(x), y) -> topA(i, N1(C(x)), y) topB(i, x, N2(y)) -> topB(i, x, N2(C(y))) topB(i, x, S2(y)) -> topB(i, x, S2(D(y))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Polynomial interpretation [POLO]: POL(0) = 0 POL(1) = 0 POL(C(x_1)) = x_1 POL(D(x_1)) = x_1 POL(N1(x_1)) = 1 + x_1 POL(N2(x_1)) = x_1 POL(S1(x_1)) = 1 + x_1 POL(S2(x_1)) = x_1 POL(T1(x_1)) = x_1
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