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TRS Standard pair #487073689
details
property
value
status
complete
benchmark
ReverseLastInit.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Applicative_05
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0583401 seconds
cpu usage
0.047491
user time
0.02686
system time
0.020631
max virtual memory
113188.0
max residence set size
5672.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S f:S g:S l:S x:S xs:S) (RULES app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) ) Problem 1: Innermost Equivalent Processor: -> Rules: app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) -> 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(compose,f:S),g:S),x:S) -> APP(f:S,x:S) APP(app(app(compose,f:S),g:S),x:S) -> APP(g:S,app(f:S,x:S)) APP(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> APP(app(reverse2,xs:S),app(app(cons,x:S),l:S)) APP(reverse,l:S) -> APP(app(reverse2,l:S),nil) -> Rules: app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) Problem 1: SCC Processor: -> Pairs: APP(app(app(compose,f:S),g:S),x:S) -> APP(f:S,x:S) APP(app(app(compose,f:S),g:S),x:S) -> APP(g:S,app(f:S,x:S)) APP(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> APP(app(reverse2,xs:S),app(app(cons,x:S),l:S)) APP(reverse,l:S) -> APP(app(reverse2,l:S),nil) -> Rules: app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APP(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> APP(app(reverse2,xs:S),app(app(cons,x:S),l:S)) ->->-> Rules: app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) ->->Cycle: ->->-> Pairs: APP(app(app(compose,f:S),g:S),x:S) -> APP(f:S,x:S) APP(app(app(compose,f:S),g:S),x:S) -> APP(g:S,app(f:S,x:S)) ->->-> Rules: app(app(app(compose,f:S),g:S),x:S) -> app(g:S,app(f:S,x:S)) app(app(reverse2,app(app(cons,x:S),xs:S)),l:S) -> app(app(reverse2,xs:S),app(app(cons,x:S),l:S)) app(app(reverse2,nil),l:S) -> l:S app(hd,app(app(cons,x:S),xs:S)) -> x:S app(reverse,l:S) -> app(app(reverse2,l:S),nil) app(tl,app(app(cons,x:S),xs:S)) -> xs:S init -> app(app(compose,reverse),app(app(compose,tl),reverse)) last -> app(app(compose,hd),reverse) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs:
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