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TRS Innermost pair #487092890
details
property
value
status
complete
benchmark
subtrees.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.020315 seconds
cpu usage
0.020854
user time
0.009129
system time
0.011725
max virtual memory
113188.0
max residence set size
5280.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S @l1:S @l2:S @t:S @t1:S @t2:S @x:S @xs:S) (RULES append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S) append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S)) append#1(nil,@l2:S) -> @l2:S subtrees(@t:S) -> subtrees#1(@t:S) subtrees#1(leaf) -> nil subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S) APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S) SUBTREES(@t:S) -> SUBTREES#1(@t:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S) SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) SUBTREES#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> APPEND(@l1:S,@l2:S) -> Rules: append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S) append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S)) append#1(nil,@l2:S) -> @l2:S subtrees(@t:S) -> subtrees#1(@t:S) subtrees#1(leaf) -> nil subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S)) Problem 1: SCC Processor: -> Pairs: APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S) APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S) SUBTREES(@t:S) -> SUBTREES#1(@t:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S) SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) SUBTREES#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> APPEND(@l1:S,@l2:S) -> Rules: append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S) append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S)) append#1(nil,@l2:S) -> @l2:S subtrees(@t:S) -> subtrees#1(@t:S) subtrees#1(leaf) -> nil subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S) APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S) ->->-> Rules: append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S) append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S)) append#1(nil,@l2:S) -> @l2:S subtrees(@t:S) -> subtrees#1(@t:S) subtrees#1(leaf) -> nil subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S)) ->->Cycle: ->->-> Pairs: SUBTREES(@t:S) -> SUBTREES#1(@t:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES(@t1:S) SUBTREES#1(node(@x:S,@t1:S,@t2:S)) -> SUBTREES#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) SUBTREES#2(@l1:S,@t1:S,@t2:S,@x:S) -> SUBTREES(@t2:S) ->->-> Rules: append(@l1:S,@l2:S) -> append#1(@l1:S,@l2:S) append#1(::(@x:S,@xs:S),@l2:S) -> ::(@x:S,append(@xs:S,@l2:S)) append#1(nil,@l2:S) -> @l2:S subtrees(@t:S) -> subtrees#1(@t:S) subtrees#1(leaf) -> nil subtrees#1(node(@x:S,@t1:S,@t2:S)) -> subtrees#2(subtrees(@t1:S),@t1:S,@t2:S,@x:S) subtrees#2(@l1:S,@t1:S,@t2:S,@x:S) -> subtrees#3(subtrees(@t2:S),@l1:S,@t1:S,@t2:S,@x:S) subtrees#3(@l2:S,@l1:S,@t1:S,@t2:S,@x:S) -> ::(node(@x:S,@t1:S,@t2:S),append(@l1:S,@l2:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: APPEND(@l1:S,@l2:S) -> APPEND#1(@l1:S,@l2:S) APPEND#1(::(@x:S,@xs:S),@l2:S) -> APPEND(@xs:S,@l2:S) -> Rules:
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