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TRS Stand 20472 pair #381714374
details
property
value
status
complete
benchmark
jw37.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n084.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.58202910423 seconds
cpu usage
3.510291616
max memory
2.23797248E8
stage attributes
key
value
output-size
3458
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(a, x), a) -> f(f(f(x, a), f(a, a)), a) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(f(a, x), a) -> f(f(f(x, a), f(a, a)), a) The set Q consists of the following terms: f(f(a, x0), a) ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(a, x), a) -> F(f(f(x, a), f(a, a)), a) F(f(a, x), a) -> F(f(x, a), f(a, a)) F(f(a, x), a) -> F(x, a) F(f(a, x), a) -> F(a, a) The TRS R consists of the following rules: f(f(a, x), a) -> f(f(f(x, a), f(a, a)), a) The set Q consists of the following terms: f(f(a, x0), a) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: F(f(a, x), a) -> F(x, a) The TRS R consists of the following rules: f(f(a, x), a) -> f(f(f(x, a), f(a, a)), a) The set Q consists of the following terms: f(f(a, x0), a)
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