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TRS Innermost pair #487092968
details
property
value
status
complete
benchmark
#4.24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0186661 seconds
cpu usage
0.019215
user time
0.004468
system time
0.014747
max virtual memory
113188.0
max residence set size
5152.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) INT(s(x:S),s(y:S)) -> INTLIST(int(x:S,y:S)) INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) -> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil Problem 1: SCC Processor: -> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) INT(s(x:S),s(y:S)) -> INTLIST(int(x:S,y:S)) INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) -> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) ->->-> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil ->->Cycle: ->->-> Pairs: INT(0,s(y:S)) -> INT(s(0),s(y:S)) INT(s(x:S),s(y:S)) -> INT(x:S,y:S) ->->-> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: INTLIST(cons(x:S,y:S)) -> INTLIST(y:S) -> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil ->Projection: pi(INTLIST) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: int(0,0) -> cons(0,nil) int(0,s(y:S)) -> cons(0,int(s(0),s(y:S))) int(s(x:S),0) -> nil int(s(x:S),s(y:S)) -> intlist(int(x:S,y:S)) intlist(cons(x:S,y:S)) -> cons(s(x:S),intlist(y:S)) intlist(nil) -> nil ->Strongly Connected Components:
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