Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487073729
details
property
value
status
complete
benchmark
32.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n181.star.cs.uiowa.edu
space
Der95
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0222549 seconds
cpu usage
0.022787
user time
0.014203
system time
0.008584
max virtual memory
113188.0
max residence set size
5600.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S v:S w:S x:S y:S z:S) (RULES choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil ) Problem 1: Innermost Equivalent Processor: -> Rules: choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: CHOOSE(x:S,cons(v:S,w:S),0,s(z:S)) -> INSERT(x:S,w:S) CHOOSE(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> CHOOSE(x:S,cons(v:S,w:S),y:S,z:S) INSERT(x:S,cons(v:S,w:S)) -> CHOOSE(x:S,cons(v:S,w:S),x:S,v:S) SORT(cons(x:S,y:S)) -> INSERT(x:S,sort(y:S)) SORT(cons(x:S,y:S)) -> SORT(y:S) -> Rules: choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil Problem 1: SCC Processor: -> Pairs: CHOOSE(x:S,cons(v:S,w:S),0,s(z:S)) -> INSERT(x:S,w:S) CHOOSE(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> CHOOSE(x:S,cons(v:S,w:S),y:S,z:S) INSERT(x:S,cons(v:S,w:S)) -> CHOOSE(x:S,cons(v:S,w:S),x:S,v:S) SORT(cons(x:S,y:S)) -> INSERT(x:S,sort(y:S)) SORT(cons(x:S,y:S)) -> SORT(y:S) -> Rules: choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: CHOOSE(x:S,cons(v:S,w:S),0,s(z:S)) -> INSERT(x:S,w:S) CHOOSE(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> CHOOSE(x:S,cons(v:S,w:S),y:S,z:S) INSERT(x:S,cons(v:S,w:S)) -> CHOOSE(x:S,cons(v:S,w:S),x:S,v:S) ->->-> Rules: choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil ->->Cycle: ->->-> Pairs: SORT(cons(x:S,y:S)) -> SORT(y:S) ->->-> Rules: choose(x:S,cons(v:S,w:S),0,s(z:S)) -> cons(v:S,insert(x:S,w:S)) choose(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> choose(x:S,cons(v:S,w:S),y:S,z:S) choose(x:S,cons(v:S,w:S),y:S,0) -> cons(x:S,cons(v:S,w:S)) insert(x:S,cons(v:S,w:S)) -> choose(x:S,cons(v:S,w:S),x:S,v:S) insert(x:S,nil) -> cons(x:S,nil) sort(cons(x:S,y:S)) -> insert(x:S,sort(y:S)) sort(nil) -> nil The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: CHOOSE(x:S,cons(v:S,w:S),0,s(z:S)) -> INSERT(x:S,w:S) CHOOSE(x:S,cons(v:S,w:S),s(y:S),s(z:S)) -> CHOOSE(x:S,cons(v:S,w:S),y:S,z:S) INSERT(x:S,cons(v:S,w:S)) -> CHOOSE(x:S,cons(v:S,w:S),x:S,v:S)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard