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SRS Relative pair #487521091
details
property
value
status
complete
benchmark
r9.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
Waldmann_06_relative
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
6.17293405533 seconds
cpu usage
21.548665886
max memory
1.343115264E9
stage attributes
key
value
output-size
2652
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 1459 ms] (2) RelTRS (3) SIsEmptyProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRoofMatchBoundsTAProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(a(b(x1))) -> b(a(a(a(b(x1))))) The relative TRS consists of the following S rules: a(a(a(x1))) -> b(b(b(b(x1)))) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : <<< POL(b(x_1)) = [[0], [0], [0], [1], [0], [0]] + [[1, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 >>> <<< POL(a(x_1)) = [[0], [0], [0], [0], [1], [0]] + [[1, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0], [0, 0, 1, 0, 0, 1], [0, 0, 0, 1, 0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: none Rules from S: a(a(a(x1))) -> b(b(b(b(x1)))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(a(b(x1))) -> b(a(a(a(b(x1))))) S is empty. ---------------------------------------- (3) SIsEmptyProof (EQUIVALENT) The TRS S is empty. Hence, termination of R/S is equivalent to termination of R. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: b(a(b(x1))) -> b(a(a(a(b(x1))))) Q is empty. ---------------------------------------- (5) QTRSRoofMatchBoundsTAProof (EQUIVALENT) The TRS R could be shown to be Match-Bounded [TAB_LEFTLINEAR,TAB_NONLEFTLINEAR] by 1. Therefore it terminates. The compatible tree automaton used to show the Match-Boundedness is represented by: final states : [0, 1] transitions: b0(0) -> 0 b0(1) -> 0 a0(0) -> 1 a0(1) -> 1 b1(0) -> 5 a1(5) -> 4
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