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TRS Stand 20472 pair #381711930
details
property
value
status
complete
benchmark
teparla3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
6.07181978226 seconds
cpu usage
15.361316273
max memory
8.1278976E8
stage attributes
key
value
output-size
13045
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) SplitQDPProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) SemLabProof [SOUND, 0 ms] (9) QDP (10) DependencyGraphProof [EQUIVALENT, 0 ms] (11) QDP (12) UsableRulesReductionPairsProof [EQUIVALENT, 0 ms] (13) QDP (14) DependencyGraphProof [EQUIVALENT, 0 ms] (15) QDP (16) PisEmptyProof [SOUND, 0 ms] (17) TRUE (18) QDP (19) QDPBoundsTAProof [EQUIVALENT, 94 ms] (20) QDP (21) PisEmptyProof [EQUIVALENT, 0 ms] (22) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(y, f(x, f(a, x))) -> f(f(a, f(x, a)), f(a, y)) f(x, f(x, y)) -> f(f(f(x, a), a), a) Q is empty. ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(y, f(x, f(a, x))) -> F(f(a, f(x, a)), f(a, y)) F(y, f(x, f(a, x))) -> F(a, f(x, a)) F(y, f(x, f(a, x))) -> F(x, a) F(y, f(x, f(a, x))) -> F(a, y) F(x, f(x, y)) -> F(f(f(x, a), a), a) F(x, f(x, y)) -> F(f(x, a), a) F(x, f(x, y)) -> F(x, a) The TRS R consists of the following rules: f(y, f(x, f(a, x))) -> f(f(a, f(x, a)), f(a, y)) f(x, f(x, y)) -> f(f(f(x, a), a), a) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 5 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(y, f(x, f(a, x))) -> F(a, y) F(y, f(x, f(a, x))) -> F(f(a, f(x, a)), f(a, y)) The TRS R consists of the following rules: f(y, f(x, f(a, x))) -> f(f(a, f(x, a)), f(a, y)) f(x, f(x, y)) -> f(f(f(x, a), a), a) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) SplitQDPProof (EQUIVALENT)
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