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TRS Relative pair #487520715
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
n139.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.16904401779 seconds
cpu usage
5.577499644
max memory
5.03230464E8
stage attributes
key
value
output-size
7033
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS S Cleaner [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 71 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 25 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 0 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 0 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
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