Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487069224
details
property
value
status
complete
benchmark
bintrees.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
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0591799 seconds
cpu usage
0.039218
user time
0.020574
system time
0.018644
max virtual memory
113188.0
max residence set size
5496.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S U:S V:S W:S X:S Y:S Z:S) (RULES concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse ) Problem 1: Innermost Equivalent Processor: -> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(U:S,V:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(W:S,Z:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S)) -> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse Problem 1: SCC Processor: -> Pairs: CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(U:S,V:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> CONCAT(W:S,Z:S) LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S)) -> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S) ->->-> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse ->->Cycle: ->->-> Pairs: LESSLEAVES(cons(U:S,V:S),cons(W:S,Z:S)) -> LESSLEAVES(concat(U:S,V:S),concat(W:S,Z:S)) ->->-> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: CONCAT(cons(U:S,V:S),Y:S) -> CONCAT(V:S,Y:S) -> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S)) lessleaves(leaf,cons(W:S,Z:S)) -> ttrue lessleaves(X:S,leaf) -> ffalse ->Projection: pi(CONCAT) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: concat(cons(U:S,V:S),Y:S) -> cons(U:S,concat(V:S,Y:S)) concat(leaf,Y:S) -> Y:S lessleaves(cons(U:S,V:S),cons(W:S,Z:S)) -> lessleaves(concat(U:S,V:S),concat(W:S,Z:S))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard