details

property	value
status	complete
benchmark	027.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n136.star.cs.uiowa.edu
space	AotoYamada_05

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.254221200943 seconds
cpu usage	0.164859796
max memory	7487488.0

stage attributes

key	value
output-size	6002
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 x:S xs:S y:S) (RULES 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) -> 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(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)) APP(inc,xs:S) -> APP(app(map,app(plus,app(s,0))),xs:S) -> Rules: 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) Problem 1: SCC Processor: -> Pairs: 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)) APP(inc,xs:S) -> APP(app(map,app(plus,app(s,0))),xs:S) -> Rules: 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) ->->-> Rules: 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) ->->Cycle: ->->-> Pairs: 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) APP(inc,xs:S) -> APP(app(map,app(plus,app(s,0))),xs:S) ->->-> Rules: 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 app(inc,xs:S) -> app(app(map,app(plus,app(s,0))),xs:S) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S) -> Rules: 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)) popout

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