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TRS Standard pair #516964761
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
n055.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0647780895233 seconds
cpu usage
0.042513165
max memory
3624960.0
stage attributes
key
value
output-size
4826
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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:
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