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SRS Standard pair #487087054
details
property
value
status
complete
benchmark
247992.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
ICFP_2010
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.9208 seconds
cpu usage
8.60729
user time
8.23629
system time
0.371007
max virtual memory
1.907558E7
max residence set size
1128468.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 146 ms] (2) QTRS (3) Overlay + Local Confluence [EQUIVALENT, 2 ms] (4) QTRS (5) DependencyPairsProof [EQUIVALENT, 10 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 3(4(5(x1))) -> 4(3(5(x1))) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(0(x_1)) = 12 + x_1 POL(1(x_1)) = 11 + x_1 POL(2(x_1)) = 24 + x_1 POL(3(x_1)) = x_1 POL(4(x_1)) = x_1 POL(5(x_1)) = x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: 0(x1) -> 1(x1) 0(0(x1)) -> 0(x1) 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(1(1(0(1(1(1(1(0(0(0(0(0(0(1(1(1(1(0(0(0(0(1(0(0(0(0(1(1(1(0(1(1(1(1(1(1(0(0(0(0(1(1(1(1(1(1(1(1(0(0(0(0(1(1(0(0(1(0(0(0(0(0(0(1(0(0(0(1(1(1(0(1(0(0(0(1(1(0(0(1(0(0(0(0(0(1(0(0(1(1(1(0(1(0(1(1(1(0(1(0(1(1(1(0(1(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(1(0(0(1(0(0(0(1(0(1(1(1(1(0(1(0(1(0(1(1(0(0(0(0(0(1(0(0(0(1(0(1(1(1(1(0(1(1(0(0(0(0(0(1(0(0(1(1(1(1(0(0(0(0(0(1(0(0(1(1(0(0(0(1(0(0(0(1(1(0(0(1(0(0(1(1(0(0(1(0(0(0(1(0(1(0(0(0(0(0(0(0(0(1(1(0(0(1(0(1(1(0(0(0(0(1(1(1(1(1(1(1(0(0(0(1(1(0(1(1(0(0(1(0(1(1(0(1(1(0(1(1(1(0(1(0(0(0(1(1(1(0(1(0(1(0(1(0(1(1(1(1(1(0(1(0(0(1(1(1(1(0(1(0(1(1(1(1(0(1(1(1(0(1(1(1(0(0(1(0(1(0(1(0(0(1(1(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(0(1(0(0(0(0(1(0(0(1(1(0(1(1(0(0(1(0(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(1(1(1(0(0(1(0(0(1(0(0(0(1(1(0(0(0(0(1(0(0(1(1(0(1(0(1(1(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(0(0(1(0(1(1(1(1(1(1(1(0(0(0(0(1(1(0(1(1(0(0(1(0(0(1(0(1(0(1(1(0(0(0(1(1(0(1(1(1(1(0(0(1(0(0(1(1(0(0(0(0(0(1(0(0(1(1(1(0(1(1(0(0(1(0(0(1(1(1(0(1(0(0(1(0(1(1(0(1(1(0(1(1(0(0(1(0(1(0(0(0(0(1(1(0(0(0(1(1(0(0(1(0(1(1(1(1(1(1(1(1(0(0(0(0(0(1(0(1(0(1(1(1(0(1(0(1(1(1(1(1(1(1(0(1(1(0(1(0(0(0(1(1(1(0(1(1(0(0(0(0(0(0(0(0(0(0(0(0(1(0(0(0(1(1(1(1(1(0(0(1(0(1(0(1(0(0(0(1(0(1(1(1(0(0(1(1(0(0(1(1(0(0(0(1(1(1(1(1(1(0(0(1(0(0(0(0(1(0(1(1(0(1(1(1(0(0(0(1(0(1(0(1(0(1(0(0(0(1(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 3(4(5(x1))) -> 4(3(5(x1))) Q is empty. ---------------------------------------- (3) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: 3(4(5(x1))) -> 4(3(5(x1))) The set Q consists of the following terms: 3(4(5(x0))) ---------------------------------------- (5) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: 3^1(4(5(x1))) -> 3^1(5(x1)) The TRS R consists of the following rules: 3(4(5(x1))) -> 4(3(5(x1)))
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