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SRS Relative pair #487521666
details
property
value
status
complete
benchmark
rel08.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
Zantema_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.15936398506 seconds
cpu usage
9.393953445
max memory
1.146765312E9
stage attributes
key
value
output-size
5196
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 132 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 2 ms] (8) RelTRS (9) RelTRSRRRProof [EQUIVALENT, 0 ms] (10) RelTRS (11) RIsEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(x1) -> x1 b(x1) -> x1 a(c(x1)) -> b(b(c(a(x1)))) d(b(b(b(x1)))) -> a(d(a(x1))) The relative TRS consists of the following S rules: a(b(x1)) -> b(a(x1)) b(a(x1)) -> a(b(x1)) ---------------------------------------- (1) RelTRS Reverse (EQUIVALENT) We have reversed the following relative TRS [REVERSE]: The set of rules R is a(x1) -> x1 b(x1) -> x1 a(c(x1)) -> b(b(c(a(x1)))) d(b(b(b(x1)))) -> a(d(a(x1))) The set of rules S is a(b(x1)) -> b(a(x1)) b(a(x1)) -> a(b(x1)) We have obtained the following relative TRS: The set of rules R is a(x1) -> x1 b(x1) -> x1 c(a(x1)) -> a(c(b(b(x1)))) b(b(b(d(x1)))) -> a(d(a(x1))) The set of rules S is b(a(x1)) -> a(b(x1)) a(b(x1)) -> b(a(x1)) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(x1) -> x1 b(x1) -> x1 c(a(x1)) -> a(c(b(b(x1)))) b(b(b(d(x1)))) -> a(d(a(x1))) The relative TRS consists of the following S rules: b(a(x1)) -> a(b(x1)) a(b(x1)) -> b(a(x1)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a(x_1)) = [[0], [0]] + [[1, 2], [0, 1]] * x_1 >>>
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