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TRS Standard pair #516967316
details
property
value
status
complete
benchmark
Ex4MapList.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n078.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.290647983551 seconds
cpu usage
0.216384534
max memory
6365184.0
stage attributes
key
value
output-size
3824
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 f:S t:S x:S) (RULES app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(cons,app(f:S,x:S)) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil Problem 1: SCC Processor: -> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(cons,app(f:S,x:S)) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S) ->->-> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil Problem 1: Reduction Pairs Processor: -> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(app(fmap,t:S),x:S) APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil -> Usable rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil ->Interpretation type: Simple mixed ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [app](X1,X2) = 2.X1.X2 + 2.X1 [cons] = 0 [fSNonEmpty] = 0 [fcons] = 2 [fmap] = 2 [fnil] = 1 [nil] = 0 [APP](X1,X2) = 2.X1.X2 + 2.X1 Problem 1: SCC Processor: -> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S) -> Rules: app(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> app(app(cons,app(f:S,x:S)),app(app(fmap,t:S),x:S)) app(app(fmap,fnil),x:S) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(fmap,app(app(fcons,f:S),t:S)),x:S) -> APP(f:S,x:S)
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