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TRS Standard pair #487067968
details
property
value
status
complete
benchmark
4.42.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.74179 seconds
cpu usage
3.79887
user time
3.63931
system time
0.159564
max virtual memory
1.8343376E7
max residence set size
229208.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 17 ms] (4) QDP (5) QDPSizeChangeProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a, g(y)) -> g(g(y)) f(g(x), a) -> f(x, g(a)) f(g(x), g(y)) -> h(g(y), x, g(y)) h(g(x), y, z) -> f(y, h(x, y, z)) h(a, y, z) -> z 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(a, g(y)) -> g(g(y)) f(g(x), a) -> f(x, g(a)) f(g(x), g(y)) -> h(g(y), x, g(y)) h(g(x), y, z) -> f(y, h(x, y, z)) h(a, y, z) -> z The set Q consists of the following terms: f(a, g(x0)) f(g(x0), a) f(g(x0), g(x1)) h(g(x0), x1, x2) h(a, x0, x1) ---------------------------------------- (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(g(x), a) -> F(x, g(a)) F(g(x), g(y)) -> H(g(y), x, g(y)) H(g(x), y, z) -> F(y, h(x, y, z)) H(g(x), y, z) -> H(x, y, z) The TRS R consists of the following rules: f(a, g(y)) -> g(g(y)) f(g(x), a) -> f(x, g(a)) f(g(x), g(y)) -> h(g(y), x, g(y)) h(g(x), y, z) -> f(y, h(x, y, z)) h(a, y, z) -> z The set Q consists of the following terms: f(a, g(x0)) f(g(x0), a) f(g(x0), g(x1)) h(g(x0), x1, x2) h(a, x0, x1) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *F(g(x), g(y)) -> H(g(y), x, g(y)) The graph contains the following edges 2 >= 1, 1 > 2, 2 >= 3
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