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SRS Standard pair #516968952
details
property
value
status
complete
benchmark
z010.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n117.star.cs.uiowa.edu
space
Zantema_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.135411977768 seconds
cpu usage
0.037677715
max memory
3121152.0
stage attributes
key
value
output-size
2759
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x1:S) (RULES a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: A(b(x1:S)) -> A(x1:S) C(b(x1:S)) -> C(c(x1:S)) C(b(x1:S)) -> C(x1:S) -> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) Problem 1: SCC Processor: -> Pairs: A(b(x1:S)) -> A(x1:S) C(b(x1:S)) -> C(c(x1:S)) C(b(x1:S)) -> C(x1:S) -> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: C(b(x1:S)) -> C(c(x1:S)) C(b(x1:S)) -> C(x1:S) ->->-> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) ->->Cycle: ->->-> Pairs: A(b(x1:S)) -> A(x1:S) ->->-> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: C(b(x1:S)) -> C(c(x1:S)) C(b(x1:S)) -> C(x1:S) -> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S))) -> Usable rules: c(b(x1:S)) -> b(c(c(x1:S))) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a](X) = 0 [c](X) = X [b](X) = X + 2 [fSNonEmpty] = 0 [A](X) = 0 [C](X) = 2.X Problem 1.1: SCC Processor: -> Pairs: C(b(x1:S)) -> C(x1:S) -> Rules: a(b(x1:S)) -> b(b(a(x1:S))) c(b(x1:S)) -> b(c(c(x1:S)))
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