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TRS Inner 89993 pair #381733613
details
property
value
status
complete
benchmark
tricky1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n038.star.cs.uiowa.edu
space
Mixed_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.71198821068 seconds
cpu usage
3.79890528
max memory
1.93245184E8
stage attributes
key
value
output-size
1865
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x)))) p(0) -> g(0) g(s(p(x))) -> p(x) The set Q consists of the following terms: f(g(x0), g(x1)) p(0) g(s(p(x0))) ---------------------------------------- (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(g(x), g(y)) -> F(p(f(g(x), s(y))), g(s(p(x)))) F(g(x), g(y)) -> P(f(g(x), s(y))) F(g(x), g(y)) -> F(g(x), s(y)) F(g(x), g(y)) -> G(s(p(x))) F(g(x), g(y)) -> P(x) P(0) -> G(0) The TRS R consists of the following rules: f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x)))) p(0) -> g(0) g(s(p(x))) -> p(x) The set Q consists of the following terms: f(g(x0), g(x1)) p(0) g(s(p(x0))) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 6 less nodes. ---------------------------------------- (4) TRUE
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