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TRS Standard pair #487067544
details
property
value
status
complete
benchmark
#3.17a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n191.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.066789 seconds
cpu usage
0.071387
user time
0.044549
system time
0.026838
max virtual memory
113188.0
max residence set size
6020.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S k:S l:S x:S y:S) (RULES app(cons(x:S,l:S),k:S) -> cons(x:S,app(l:S,k:S)) app(nil,k:S) -> k:S app(l:S,nil) -> l:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) pred(cons(s(x:S),nil)) -> cons(x:S,nil) sum(app(l:S,cons(x:S,cons(y:S,k:S)))) -> sum(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) sum(plus(cons(0,x:S),cons(y:S,l:S))) -> pred(sum(cons(s(x:S),cons(y:S,l:S)))) sum(cons(x:S,cons(y:S,l:S))) -> sum(cons(plus(x:S,y:S),l:S)) sum(cons(x:S,nil)) -> cons(x:S,nil) ) Problem 1: Dependency Pairs Processor: -> Pairs: APP(cons(x:S,l:S),k:S) -> APP(l:S,k:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> APP(l:S,sum(cons(x:S,cons(y:S,k:S)))) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> SUM(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> SUM(cons(x:S,cons(y:S,k:S))) SUM(plus(cons(0,x:S),cons(y:S,l:S))) -> PRED(sum(cons(s(x:S),cons(y:S,l:S)))) SUM(plus(cons(0,x:S),cons(y:S,l:S))) -> SUM(cons(s(x:S),cons(y:S,l:S))) SUM(cons(x:S,cons(y:S,l:S))) -> PLUS(x:S,y:S) SUM(cons(x:S,cons(y:S,l:S))) -> SUM(cons(plus(x:S,y:S),l:S)) -> Rules: app(cons(x:S,l:S),k:S) -> cons(x:S,app(l:S,k:S)) app(nil,k:S) -> k:S app(l:S,nil) -> l:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) pred(cons(s(x:S),nil)) -> cons(x:S,nil) sum(app(l:S,cons(x:S,cons(y:S,k:S)))) -> sum(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) sum(plus(cons(0,x:S),cons(y:S,l:S))) -> pred(sum(cons(s(x:S),cons(y:S,l:S)))) sum(cons(x:S,cons(y:S,l:S))) -> sum(cons(plus(x:S,y:S),l:S)) sum(cons(x:S,nil)) -> cons(x:S,nil) Problem 1: SCC Processor: -> Pairs: APP(cons(x:S,l:S),k:S) -> APP(l:S,k:S) PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> APP(l:S,sum(cons(x:S,cons(y:S,k:S)))) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> SUM(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) SUM(app(l:S,cons(x:S,cons(y:S,k:S)))) -> SUM(cons(x:S,cons(y:S,k:S))) SUM(plus(cons(0,x:S),cons(y:S,l:S))) -> PRED(sum(cons(s(x:S),cons(y:S,l:S)))) SUM(plus(cons(0,x:S),cons(y:S,l:S))) -> SUM(cons(s(x:S),cons(y:S,l:S))) SUM(cons(x:S,cons(y:S,l:S))) -> PLUS(x:S,y:S) SUM(cons(x:S,cons(y:S,l:S))) -> SUM(cons(plus(x:S,y:S),l:S)) -> Rules: app(cons(x:S,l:S),k:S) -> cons(x:S,app(l:S,k:S)) app(nil,k:S) -> k:S app(l:S,nil) -> l:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) pred(cons(s(x:S),nil)) -> cons(x:S,nil) sum(app(l:S,cons(x:S,cons(y:S,k:S)))) -> sum(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) sum(plus(cons(0,x:S),cons(y:S,l:S))) -> pred(sum(cons(s(x:S),cons(y:S,l:S)))) sum(cons(x:S,cons(y:S,l:S))) -> sum(cons(plus(x:S,y:S),l:S)) sum(cons(x:S,nil)) -> cons(x:S,nil) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) ->->-> Rules: app(cons(x:S,l:S),k:S) -> cons(x:S,app(l:S,k:S)) app(nil,k:S) -> k:S app(l:S,nil) -> l:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) pred(cons(s(x:S),nil)) -> cons(x:S,nil) sum(app(l:S,cons(x:S,cons(y:S,k:S)))) -> sum(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) sum(plus(cons(0,x:S),cons(y:S,l:S))) -> pred(sum(cons(s(x:S),cons(y:S,l:S)))) sum(cons(x:S,cons(y:S,l:S))) -> sum(cons(plus(x:S,y:S),l:S)) sum(cons(x:S,nil)) -> cons(x:S,nil) ->->Cycle: ->->-> Pairs: SUM(cons(x:S,cons(y:S,l:S))) -> SUM(cons(plus(x:S,y:S),l:S)) ->->-> Rules: app(cons(x:S,l:S),k:S) -> cons(x:S,app(l:S,k:S)) app(nil,k:S) -> k:S app(l:S,nil) -> l:S plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) pred(cons(s(x:S),nil)) -> cons(x:S,nil) sum(app(l:S,cons(x:S,cons(y:S,k:S)))) -> sum(app(l:S,sum(cons(x:S,cons(y:S,k:S))))) sum(plus(cons(0,x:S),cons(y:S,l:S))) -> pred(sum(cons(s(x:S),cons(y:S,l:S)))) sum(cons(x:S,cons(y:S,l:S))) -> sum(cons(plus(x:S,y:S),l:S)) sum(cons(x:S,nil)) -> cons(x:S,nil) ->->Cycle: ->->-> Pairs: APP(cons(x:S,l:S),k:S) -> APP(l:S,k:S) ->->-> Rules:
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