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TRS Standard pair #487072768
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n179.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
4.41815 seconds
cpu usage
9.44557
user time
9.02812
system time
0.41745
max virtual memory
1.8617272E7
max residence set size
599372.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) QDPOrderProof [EQUIVALENT, 25 ms] (12) QDP (13) QDPOrderProof [EQUIVALENT, 235 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: c(c(c(y))) -> c(c(a(y, 0))) c(a(a(0, x), y)) -> a(c(c(c(0))), y) c(y) -> y 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: C(c(c(y))) -> C(c(a(y, 0))) C(c(c(y))) -> C(a(y, 0)) C(a(a(0, x), y)) -> C(c(c(0))) C(a(a(0, x), y)) -> C(c(0)) C(a(a(0, x), y)) -> C(0) The TRS R consists of the following rules: c(c(c(y))) -> c(c(a(y, 0))) c(a(a(0, x), y)) -> a(c(c(c(0))), y) c(y) -> y 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 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: C(c(c(y))) -> C(a(y, 0)) C(a(a(0, x), y)) -> C(c(c(0))) C(c(c(y))) -> C(c(a(y, 0))) C(a(a(0, x), y)) -> C(c(0)) The TRS R consists of the following rules: c(c(c(y))) -> c(c(a(y, 0))) c(a(a(0, x), y)) -> a(c(c(c(0))), y) c(y) -> y Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule C(a(a(0, x), y)) -> C(c(0)) at position [0] we obtained the following new rules [LPAR04]: (C(a(a(0, y0), y1)) -> C(0),C(a(a(0, y0), y1)) -> C(0)) ---------------------------------------- (6) Obligation:
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