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TRS Standard pair #516965041
details
property
value
status
complete
benchmark
011.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n112.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.600438833237 seconds
cpu usage
0.506667108
max memory
7458816.0
stage attributes
key
value
output-size
10342
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S f:S g:S x:S xs:S y:S) (RULES app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) -> 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(app(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y:S) -> APP(g:S,x:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) Problem 1: SCC Processor: -> Pairs: APP(app(app(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y:S) -> APP(g:S,x:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(cons,app(f:S,x:S)) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S)) -> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) ->->-> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) ->->Cycle: ->->-> Pairs: APP(app(app(curry,g:S),x:S),y:S) -> APP(app(g:S,x:S),y:S) APP(app(app(curry,g:S),x:S),y:S) -> APP(g:S,x:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(app(map,f:S),xs:S) APP(app(map,f:S),app(app(cons,x:S),xs:S)) -> APP(f:S,x:S) ->->-> Rules: app(app(app(curry,g:S),x:S),y:S) -> app(app(g:S,x:S),y:S) app(app(map,f:S),app(app(cons,x:S),xs:S)) -> app(app(cons,app(f:S,x:S)),app(app(map,f:S),xs:S)) app(app(map,f:S),nil) -> nil app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S)) app(app(plus,0),y:S) -> y:S inc -> app(map,app(app(curry,plus),app(s,0))) The problem is decomposed in 2 subproblems.
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